We, of course, had civilian doctors for our son and really did not do any research other than to take other physicians approval of the surgeons involved, plus the fact that they were employed by Kaiser. So our "competence check" was pretty sketchy.
Having said that, after 20+ years dealing with Navy medicine here is my thoughts about military doctors. While you can have idiots in any field and I have heard the usual horror stories of wrong knees operated on and so forth, I have exactly the same level of confidence in military medicine as I do civilian. Here are some good reasons. The majority of operational military doctors are in the prime of their careers, young enough to be up on the newest procedures taught in med school but old enough to have a bunch of experience. There is also a lot of teaching going on but that means lots of supervision. The military hates failure and wants to keep its members active and functional so there is big pressure for successful outcomes. Facial surgery plays right into battle wounds and as a result, I would expect excellent bone surgeons using the newest and best procedures to be looking at your daughter.
If you want to look at the most gloomy result, if there were problems (very, very unlikely) it most likely would have happened in a civilian setting just as well. Only in the AF, the government now has that problem to solve or remedy permanently. They cannot just say "Oops, have a nice life" and send a service member out the door. You won't get that lifetime accountability in a civilian operation.
As far as academics, I would leave that as your daughter's problem and there is plenty of precedent for medical recovery and class work. She won't be the first cadet contending with surgery. If anything, she will be able to concentrate on academics MORE than she ever did before as all the military stuff is off the table. That challenge will solve itself.
The big thing is: does she want the problem solved badly enough to go through the surgery. If she doesn't, I'd leave it alone until it becomes so bothersome she doesn't want to live with it anymore and let HER make the decision to initiate things. She can have this surgery at anytime during her AF career.
(We are just noticing that our son's 6 year-old little boy has that same charming lopsided smile and misaligned front teeth. Looks like de ja vu all over again!)