Anything with psych for an MEB will take some time. Why? It is not so cut and dry. It is not like looking at an MRI and saying "Wow, there is the problem!" When you see a psychiatrist it takes several visits and discussions before they can start forming a diagnosis. You can try and come outright and say what your issue is but they will not listen. They need to make their own informed decision. Many mental conditions are alike or contain like-symptoms and so the MD has to gather all evidence before making a proper diagnosis. Next is to figure out how the diagnosis impairs you. You also have to begin treatment. In almost all cases comes medications. This is part of the treatment phase. Imagine breaking your leg and having to do physical therapy after surgery to fix it. Your considered unstable. Once meds are set, which is a lot of trial and error, drug changes, dosage tinkering, and once treatment is pretty far along, complete, diagnosis is made, established, and well documented, then they determine if you are retainable or not. If not, then they will write up paperwork requesting an MEB. They can also do tests as well. Blot tests, Q&A, situational discussions, etc.
Some things that do speed this up are if your conditions are so serious they require hospitalization because those are instant MEBs. You do still have to go through the whole treatment phase, proper diagnosis, etc. but no matter what, because you required hospitalization, you'll be going to the MEB and they start the paperwork and decision usually while your in the hospital or starting treatment.