Barn,
I foresee a few problems. First off, although an airlift background is no bar to TP (at any of the establishments I am aware of) - lack of a FJ medical is. Multi guys fly fighters various on the course and therefore need to have the medical 'ticket' for it.
From a military perspective, if you have an appropriate medical, the right experience and the right quals then you can apply for TP. There is a lot of competition to even get invited for selection, you then have to get through selection (and the course!).
You need to pass a more stringent medical than FJ for astronaut selection. I can provide you some very detailed info on the medical for (NASA) astronaut selection if you wish to see the standards etc.
Is there any way they can fix/patch/mitigate your condition? It's probably worth investigating (I have no medical training so I have no idea).
Cheers,
MT