I would imagine no matter the service, they should be sending you to a U.S. doctor for an exam/opinion. I would continue to push that... In fact, it is always your right as a patient to request a second opinion. The first cardiologist to tell me I needed surgery was a civilian doctor. When that info got to TRICARE they required me to see a military doc and then I consulted with a second military doc after that.
In the Navy when you're suffering from a major medical condition, you're enrolled in the Navy Wounded Warrior/Safe Harbor program. You're assigned an advocate to assist you through the recovery process. Also, separately, you're assigned a nurse case manager to assist you in getting appointments, prescriptions, medical device(s), etc. When I was considering having the procedure done at Walter Reed, my Navy Safe Harbor advocate was coordinating a little apartment-type place for myself and a caretaker to stay until I was safe to fly. It was going to be at no cost to me. There has to be some sort of equivalent for the Air Force.
As far as the MEB/PEB, I had my surgery done in the end of May. I returned to work in the end of June. I requested my PCM initiate the MEB/PEB immediately because I want to know what the future looks like for me as far as my career goes. If I'm able to stay, great. If not, then I want to make the transition into the next phase of life. Anyway, my board was initiated in early July. I met with my PEBLO and consulted with the military disability attorney by mid-July. I had my VA rep appointment to go over all of my ailments and to submit my VA claim in late-July. My C&P exams were about a week ago. Thats where I currently stand... The next step is for my PEBLO to receive my packet from the VA. Once they get it, they'll send that package, my non-medical assessment from my command, and the narrative summary from my PCM to the PEB in DC. Then it's a waiting game for the fit/unfit decision. During this process, you can't go TDY or on leave that takes you away from your permanent duty station area.
I've been told by several docs the mechanical valve was the right choice due to my age (early 30s), but that I pretty much guaranteed an "unfit" decision from the PEB. To me that's ok. I would rather make the best choice for my health and be here to see my child grow up.
If you have anymore questions, let me know. If not, I'll post updates about my PEB here so you can see.