So, I've got SkyRe and Immersive Armors installed as well as the Reproccer and a Wrye Bash patch. Now, my problem is that I picked up an Elvish Gilded Armor from a chest and it was worse than Mercenary Armor. It doesn't seem to make sense to me that a leather armor would be superior to Elvish armor since SkyRe has Elvish armor above Leather armor on the Smithing perk tree. For the record, the Mercenary Armor was at 74 armor and the Elvish armor was at 43 armor. Someone on Reddit suggested I move the ReProccer above the ESP for Immersive Armors. I did so, but it seemed to revert my armor values to near vanilla. Now the Mercenary armor has an armor value of 32 and the Elvish armor still has an armor value of 43. Is there some kind of reference table for SkyRe + Immersive Armors so I can check which set of values is closer to "working as intended"?

Reproccer should definitely load very late, in your case after the Bashed Patch - and often dead last. Something is up with your game and it might perhaps be the load order (just guessing as I of course have no idea based on the above information). I'm using both IA and SkyRe and when checking it in TES5Edit, Mercenary Armor goes from 31 in IA to 60 in Reproccer, while Elven Gilded Armor goes from 35 to 75.

You can check which mod that affects what with TES5Edit. Just load it with all plugins you are using and check under Skyrim.esm > Armor and Hothtrooper44_ArmorCompilation.esp > Armor in this case.

My guess is that it's a case of wrong load ordering, which would be fixed if you run LOOT and then rerun the Reproccer patch.