Sarah, I really appreciate your thoughtful response. I have definitely learned things from applying this year that would make me a better candidate, but I do not know if I really want to get rejected again, as well as hunt down all the teachers that gave me a LOR and ask again. At this point in my academic career I am not sure what I want to do, but I feel that enlisting may be my best option. Civilian life just isn't my thing, and I do not think that a civilian college would help me any either. I will be talking to a recruiter over the next couple weeks, and hopefully they will offer me something/show me a path that is even better than the one that the service academies offered--I have found a new interest in the Navy's Nuclear Operations program. It has prestige and seems to be an academic challenge, as well as a good education in the STEM field that I am so interested in.
I have emailed my AO and hopefully he will give me some critical advice, and if I see that there really was a big hole in my application, then I will reapply. Good luck in your military career.