As usual when playing Morrowind, the game can crash at any random moment. Every time I play Morrowind I fear this impending crash, and do save at any given moment so I don't lose anything. However, instead of trying to just live with it, I need to try and figure out a way to get rid of these crashes entirely. I've read the sticky, and none of what is there helps me. The crashes are tiresome, and I need to seek for more solutions. They become more often every occurring day I play my character (which is fairly new).

Are there any other tricks, or just anything I can do to attempt to remove or lessen these crashes? I know it's not a mod, or hardware problem. It's definitely the game itself. What can I do?

First of all, does your Warning.txt ever have a list of errors after a crash? They can help you pinpoint if there's a in-game problem.

Do you use mods? How about external mod programs, like MWE or MGE?
Is your Load Order healthy? And is your Save file clean?
http://code.google.com/p/mlox/wiki/Mlox can help organize your Load Order, and http://www.tesnexus.com/downloads/file.php?id=27588 can keep your esps and Save files updated and repaired.

Many people seem to find an increase in stability after installing the http://www.tesnexus.com/downloads/file.php?id=19510. (it's a great patch to have regardless)
Same with the http://www.ntcore.com/4gb_patch.php.

Finally, perhaps your computer is old/weak and isn't able to handle the game... although this is doubtful since almost any computer made in the last 8 years should be fine to run the game with normal settings.

One other tip...
Make a new Save file after every five saves or so. (delete the old saves as they pile up... too many can cause problems)

I use MGE, and few minor mods. My load order is sorted, and my save file is 100% clean. I do have the Code Patch, and my computer is more than good to run Morrowind. I'll apply the 4gb patch and see what it does for me. For now, this is all I've gotten from my warnings:
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XCenturion_Bomb.NIF" tex not found "Textures\plx_crt\Spider_Bomb1.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XCenturion_Bomb.NIF" tex not found "Textures\plx_crt\Spider_Bomb2.dds"!
Texture Load Error!: Textures\plx_crt\Spider_Bomb1.dds
Texture Load Error!: Textures\plx_crt\Spider_Bomb2.dds
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XCenturion_Repair.NIF" tex not found "tx_dwrv_lens00.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XCenturion_Repair.NIF" tex not found "tx_dwrv_lens00.dds"!
Texture Load Error!: tx_dwrv_lens00.dds
NiAnimation Error: Object "ManeBone01" not found in NiAnimation.
Unable to LayerActivate for AnimGroup "Idle" for "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XCenturion_Repair.NIF".
NiAnimation Error: Object "ManeBone01" not found in NiAnimation.
Unable to LayerActivate for AnimGroup "Idle2" for "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XCenturion_Repair.NIF".
NiAnimation Error: Object "ManeBone01" not found in NiAnimation.
Unable to LayerActivate for AnimGroup "Idle3" for "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XCenturion_Repair.NIF".
NiAnimation Error: Object "ManeBone01" not found in NiAnimation.
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XCenturion_Repair.NIF" tex not found "tx_dwrv_lens00.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XCenturion_Repair.NIF" tex not found "tx_dwrv_lens00.dds"!
Texture Load Error!: tx_dwrv_lens00.dds
Texture Load Error!: TX_Steam_Centurion_00.tga
Texture Load Error!: TX_Creature_GoldSipder02.tga
Texture Load Error!: TX_Creature_GoldSipder03.tga
Texture Load Error!: TX_Creature_GoldSipder04.tga
Texture Load Error!: TX_Steam_Centurion_17.tga
Texture Load Error!: TX_SphereArcher_00.dds
Texture Load Error!: TX_Steam_Centurion_15.tga
Texture Load Error!: TX_Steam_Centurion_24.tga
Texture Load Error!: TX_Steam_Centurion_19.tga
Texture Load Error!: TX_Steam_Centurion_18.tga
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\DwarvenBolt.nif" tex not found "Textures\plx_crt\DwarvenBolt.bmp"!
Texture Load Error!: Textures\plx_crt\DwarvenBolt.bmp
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Slave_A.NIF" tex not found "Textures\plx_crt\6th_robe_black_lb.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Slave_A.NIF" tex not found "Textures\plx_crt\6th_robe_black_lb.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Slave_A.NIF" tex not found "Tx_wood_6th_redblock.tga"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Slave_A.NIF" tex not found "Textures\plx_crt\hos_a_6th_helmetmask.dds"!
Texture Load Error!: Textures\plx_crt\6th_robe_black_lb.dds
Texture Load Error!: Tx_wood_6th_redblock.tga
Texture Load Error!: Textures\plx_crt\hos_a_6th_helmetmask.dds
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "TX_Skeleton_clavicle.BMP"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "TX_Skeleton_scapula.BMP"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Tx_metal_6th_bells.tga"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Tx_glass_6th_ashaltar.tga"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Tx_metal_6th_bells.tga"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Tx_glass_6th_ashaltar.tga"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6th_cuirass.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6th_ulaf.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6th_chestpiece.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6th_helmetmask.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6th_ncloth.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_pauldron00.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_02.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_pauldron00.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_02.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6th_ncloth.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\MCA_Ash_Warrior.NIF" tex not found "Textures\plx_crt\HoS_a_6thArmour_general_01.dds"!
Texture Load Error!: TX_Skeleton_clavicle.BMP
Texture Load Error!: TX_Skeleton_scapula.BMP
Texture Load Error!: Textures\plx_crt\HoS_a_6thArmour_general_01.dds
Texture Load Error!: Tx_metal_6th_bells.tga
Texture Load Error!: Tx_glass_6th_ashaltar.tga
Texture Load Error!: Textures\plx_crt\HoS_a_6th_cuirass.dds
Texture Load Error!: Textures\plx_crt\HoS_a_6th_ulaf.dds
Texture Load Error!: Textures\plx_crt\HoS_a_6th_chestpiece.dds
Texture Load Error!: Textures\plx_crt\HoS_a_6th_helmetmask.dds
Texture Load Error!: Textures\plx_crt\HoS_a_6th_ncloth.dds
Texture Load Error!: Textures\plx_crt\HoS_a_6thArmour_pauldron00.dds
Texture Load Error!: Textures\plx_crt\HoS_a_6thArmour_general_02.dds
Texture Load Error!: Textures\plx_crt\HoS_a_6thArmour_general_01.dds
Texture Load Error!: TX_Skeleton_clavicle.BMP
Texture Load Error!: Textures\plx_crt\HoS_a_6thArmour_pauldron00.dds
Texture Load Error!: Textures\plx_crt\HoS_a_6thArmour_general_02.dds
Texture Load Error!: TX_Skeleton_scapula.BMP
Texture Load Error!: Tx_metal_6th_bells.tga
Texture Load Error!: Tx_glass_6th_ashaltar.tga
Texture Load Error!: Textures\plx_crt\HoS_a_6th_cuirass.dds
Texture Load Error!: Textures\plx_crt\HoS_a_6th_ulaf.dds
Texture Load Error!: Textures\plx_crt\HoS_a_6th_chestpiece.dds
Texture Load Error!: Textures\plx_crt\HoS_a_6th_helmetmask.dds
Texture Load Error!: Textures\plx_crt\HoS_a_6th_ncloth.dds
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\6th_Longsword.nif" tex not found "Textures\plx_crt\6th_iron_blade.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\6th_Longsword.nif" tex not found "Textures\plx_crt\6th_Sword_Guard.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\6th_Longsword.nif" tex not found "Textures\plx_crt\6th_Sword_Filler.dds"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\6th_Longsword.nif" tex not found "Textures\plx_crt\6th_Sword_Grip.dds"!
Texture Load Error!: Textures\plx_crt\6th_iron_blade.dds
Texture Load Error!: Textures\plx_crt\6th_Sword_Guard.dds
Texture Load Error!: Textures\plx_crt\6th_Sword_Filler.dds
Texture Load Error!: Textures\plx_crt\6th_Sword_Grip.dds
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XMCA_Ash_Priest.NIF" tex not found "Textures\plx_crt\_ground_Sleeper_01.bmp"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XMCA_Ash_Priest.NIF" tex not found "Textures\plx_crt\_tassels_02.bmp"!
Texture Load Error!: Textures\plx_crt\_ground_Sleeper_01.bmp
Texture Load Error!: Textures\plx_crt\_tassels_02.bmp
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XMCA_Ash_Priest.NIF" tex not found "Textures\plx_crt\_ground_Sleeper_01.bmp"!
TES3Stream Warning: Model "C:\Games\Morrowind\Data Files\Meshes\plx_crt\XMCA_Ash_Priest.NIF" tex not found "Textures\plx_crt\_tassels_02.bmp"!
Texture Load Error!: Textures\plx_crt\_ground_Sleeper_01.bmp
Texture Load Error!: Textures\plx_crt\_tassels_02.bmp
-----
Here's my MOD LIST:
[Game Files]
GameFile0=Better Heads Bloodmoon addon.esm
GameFile1=Better Heads Tribunal addon.esm
GameFile2=Better Heads.esm
GameFile3=Bloodmoon.esm
GameFile4=MCA.esm
GameFile5=Morrowind Patch v1.6.4.esm
GameFile6=Morrowind.esm
GameFile7=Texture Fix - Bloodmoon 1.1.esm
GameFile8=Texture Fix 1.8.esm
GameFile9=Tribunal.esm
GameFile10=TR_Data.esm
GameFile11=TR_Map1.esm
GameFile12=TR_Map2.esm
GameFile13=abotWhereAreAllBirdsGoing.esp
GameFile14=AEV_TCA.esp
GameFile15=Animated Morrowind 1.0.esp
GameFile16=Animated Morrowind II.esp
GameFile17=Animated_Morrowind - Expanded.esp
GameFile18=Antares' Creatures - Trolls!.esp
GameFile19=Balance - Character.esp
GameFile20=Balance - game settings.esp
GameFile21=Balance - items.esp
GameFile22=Balance - Magic Effects.esp
GameFile23=Balance - NPC Spellcasting.esp
GameFile24=Balance - spells.esp
GameFile25=Better Bodies.esp
GameFile26=Better Clothes_v1.1.esp
GameFile27=Census and Excise Office.esp
GameFile28=Clean Ultimate Morrowind Anti-Mod.esp
GameFile29=Creatures 6th House Patch.esp
GameFile30=Creatures.esp
GameFile31=EcoAdj Ingredients.esp
GameFile32=EcoAdjCrime (Tresspass Edit).esp
GameFile33=EcoAdjCrime.esp
GameFile34=EcoAdjDaedricDrops.esp
GameFile35=EcoAdjMerchantSkills (Disposition Edit).esp
GameFile36=EcoAdjMerchantSkills.esp
GameFile37=EcoAdjMisc.esp
GameFile38=Galsiahs Character Development.esp
GameFile39=Gameplay - Dialogue.esp
GameFile40=Gameplay - Faction.esp
GameFile41=GCD better balanced birthsigns.esp
GameFile42=GCD Restore Potions Fix.esp
GameFile43=GCD StartScript for Trib or Bloodmoon.esp
GameFile44=LGNPC_Aldruhn_v1_20.esp
GameFile45=LGNPC_Aldruhn_v1_20_suppl.esp
GameFile46=LGNPC_AldVelothi_v1_20.esp
GameFile47=LGNPC_GnaarMok_v1_10.esp
GameFile48=LGNPC_HlaOad_v1_32.esp
GameFile49=LGNPC_IndarysManor_v1_51.esp
GameFile50=LGNPC_Khuul_v2_10.esp
GameFile51=LGNPC_MaarGan_v1_20.esp
GameFile52=LGNPC_NoLore_v0_83.esp
GameFile53=LGNPC_PaxRedoran_v1_20.esp
GameFile54=LGNPC_Pelagiad_v1_22.esp
GameFile55=LGNPC_SecretMasters_MCA5.esp
GameFile56=LGNPC_SecretMasters_v1_30.esp
GameFile57=Lgnpc_SN.esp
GameFile58=LGNPC_SoulSicknessPatch_v1_00.esp
GameFile59=LGNPC_TelMora_v1_20.esp
GameFile60=LGNPC_TelUvirith_v1_20.esp
GameFile61=LGNPC_TelUvirith_v1_20_UI.esp
GameFile62=LGNPC_VivecFQ_v2_10.esp
GameFile63=LGNPC_VivecRedoran_v1_50.esp
GameFile64=MCA - Guards Patch.ESP
GameFile65=MCA - TR Addon.ESP
GameFile66=More Better Clothes.ESP
GameFile67=NoM 3.0.esp
GameFile68=NX9_Guards_Complete.ESP
GameFile69=Nymeria's Faster Walk.esp
GameFile70=Scatter Mod (with Loot Balance).esp
GameFile71=Sixth House.esp
GameFile72=Starfires NPC Additions ver-1.11.esp
GameFile73=Texture Fix -TR -1.0.esp
GameFile74=Undead arise from death 2.0.esp
GameFile75=Westly's Master Headpack X.esp

Almost all your warnings are very serious.
Especially the Animation errors, they usually always cause a crash.

You seem to have incorrectly installed at least two mods (MCA, Sixth House, possibly Creatures) because the game can't find the files it needs.

I'll try reinstalling those, but are there any other utilities that can help me with the problem further? (such as cleaning up the problems or pin pointing what needs to be fixed)

I suggest that use you http://www.fliggerty.com/phpBB3/viewtopic.php?f=53&t=3646 (non-python) instead of Wrye Mash (python-based) to check out if a mod has any missing masters or not.

Other than that just follow Pluto's suggested advice for a solution of your CTD issue.