You have more resources than most civilian students. Go to a school that will lets you train in a multi-engine at the private pilot level. I would argue this takes priority over the MEI rating. Unless you end up teaching at pilot mill like ATP or at a provider that contracts with Chinese students - it would be hard to instruct as MEI. The reason is the many other instructors that are competing to get the prized ME time and not many students wanting to pay to fly the ME since flight training is already expensive. Yes, there are Community Colleges that will allow you to do training in a ME aircraft (I went to one) - although most will be restrictive or reluctant because of perceived abuse. Doing it as a private pilot is the fastest way to reach 50+ ME hours. And if you decide not to be an instructor, you have the hours you need. Heres what I did:

Private Single
Private Multi Add-On (To act/log time as PIC of ME)
Instrument in Multi (build ME-time here)
Commercial Multi (build ME-time here)
Commercial Single Add-on

Renting a complex aircraft with retractable gear was almost as much as multi-engine aircraft anyway at my flight school. It made more sense to fly the ME and using a bit more of your flight lab funds because you CAN with the GI Bill and you need it anyway. Once you get your Commercial Multi, you can do you Single-Engine add-on in a fixed gear since you demonstrated complex operations in the multi. This is where you save money in your flight lab. There is always the option of transferring to another Community College during the Summer term just doing your MEI there (like Northern Michigan College) - ensure you don't finish your degree or leave one class at you parent school to finish at NMC which you can transfer credits back and graduate. Most community college will have flexible admissions especially during the Summer time. Its YOUR benefits, so you can plan and use it as long as it leads to a degree.

Believe me, by doing this you will have a lot more flexibility with planning your career because you are not chasing ME time.