First, don't panic, you'll definitely get your passport.
My brother just went a few weeks ago to turn in his paperwork, get the photos, etc. He already got it back. They didn't even do the expedited process. We're still not quite into that summer crunch phase so you're lucky. But I would go as soon as possible. I prefer going to the post office. Some of them will throw in free overnight or priority shipping if you pay the $10 for them to take your passport photos. Definitely a plus there. Plus the post office can usually give you a good timeline of what it will take to get it back. Mine told me 6 and I got it in 3 back in October.
If you are really worried though, get the expedited process for the extra money. 3 months out should be plenty of time to make that happen.
As for the passport facilities, you can only go there if you need a same day passport or you are leaving in less than 2 weeks I believe. I don't think they could help you out now.
As a total last resort I'd call your Congressmen and tell them that you are a proud vet who just served her country in Afghanistan and they better hook you up. They might be able to cut through some of the red tape with the passport agency. Stress you're a vet AND a registered voter eagerly anticipating the November elections. But again, thats with like 10 days to go or less.