I have just the same issue, and I've gone through my load order checking each mod one by one. The game starts fine when it's just Fallout.esm and the DLC esms, but whenever I add any number of mods to it, it doesn't work. I've been through my load order with just Fallout.esm and each individual mod (and necessary masters) one by one and it worked perfectly on every one. This has lead me to be convinced that it isn't a load order problem, but rather something to do with the game itself. So I un and reinstalled it. Performed the same tests again and had the same issue.

What do?

Also, here's my load order, in case I've missed something.

Fallout3.esm
ThePitt.esm
BrokenSteel.esm
Zeta.esm
CRAFT.esm
CALIBR.esm
FO3 Wanderers Edition - Main File.esm
Unofficial Fallout 3 Patch.esm
MTC Wasteland Travellers.esp
Savage Wasteland - Fewer Gun Wielding Maniacs.esp
MTC Wasteland Travellers (Optional)- Crowded Cities.esp
MTC Wasteland Travellers (Optional)- Crowded Cities less NPCs.esp
RobCo Certified.esp
Wasteland Whisperer.esp
Portable Tent.esp
UPP - Pack 1.esp
CASM.esp
Rude Awakening.esp
WeaponModKits.esp
Unofficial Fallout 3 Patch - The Pitt.esp
Unofficial Fallout 3 Patch - Broken Steel.esp
CRAFT - Activation Perk.esp
FO3 Wanderers Edition - Main File.esp
FO3 Wanderers Edition - DLC The Pitt.esp
FO3 Wanderers Edition - DLC Broken Steel.esp
FO3 Wanderers Edition - DLC Mothership Zeta.esp
FO3 Wanderers Edition - Followers Enhanced (BrokenSteel).esp
FO3 Wanderers Edition - Alternate Travel.esp
FO3 Wanderers Edition - Optional Worn Weapons.esp
FO3 Wanderers Edition - Optional Restore Tracers.esp
FO3 Wanderers Edition - Optional Restore Tracers (automatics only).esp
FO3 Wanderers Edition - Optional VATS Realtime.esp
FO3 Wanderers Edition - UFP Support.esp

Total active plugins: 33
Total plugins: 38

The reason the menu isn't appearing when you use WMK-FWE is because the compatibility patch will be trying to reference a FormList (At least, that's the culprit record iirc) that is not present anymore, probably because you updated your version of FWE/ the WMK CP is outdated and the FormID's of the FLSTs have been shuffled around.