FSU Pilot-
In my opinion, you're not going to get this cleared up through emails and calling. However, I don't think you should give up.
You have not indicated, and I am assuming that you don't have a current employee on the inside to vouch for you. If you do, this person will need to make a personal trip to their office on your behalf.
If you don't know anyone on the inside, all hope is not lost. What you'll need to do is attend MORE than one job fair that they will be at within the next few months. That way, you get face time with an HR representative. Be candid and open about your mistake. Also explain to them how much you want this job, and that you traveled all this way just to talk to them. I am willing to bet they'll take another look at you.
Best of luck!
Z