Sorry to hear about this.
I don't think it would be a show-stopper at an airline, but they're going to want details about your (potential) discharge. Make sure you keep working on being in the best shape possible for your possible future interview - airlines (at least at DL) seem to hang a lot of credibility on the image of their cockpit crews. Don't give them a reason not to hire you if it's between you and someone else.
I hope you can work something out with your CC...there's a lot of time and resources being thrown away if they go through with this. What pinhead came up with this policy? I can appreciate keeping the troops in shape, but a case like yours sounds like one which should be taken on a case-by-case basis.
I feel for ya - I'm almost 6'4" and 210 lbs with a wierd shape - no gut, but wide hips which translates to a 38" pants in the waistline. That's what my DNA dealt me, so all the ab crunchers and torso twists in the world aren't going to change it.
Good luck & thanks for your service.