To the OP before you become too discouraged from the latest replies:
believe the stats you have posted make you a very competitive candidate **on your own merit**. Keep working on those things and those things alone (without the connections) and *YOU* will feel like you have deserved the nomination and appointment if they are given. You are in a competitive district, no doubt about that. However, if you are competitive enough for an appointment, trust the system to work the way it is intended and it will work out for the best of everyone.
Since it is important to maintain a sense of balance here, think about how you would feel if tables were turned and another less deserving (or even equivalently deserving) candidate got in and you did not because a few strings were pulled. That would hurt both candidates: one who was deserving and didn't quite make the cut, and the other who got in because of connections who might regret the decision when the going gets really tough.
Interestingly, many well-meaning but unlearned people insinuated that my son would have a hard time getting a nomination because we didn't personally know the politicians. What we learned, however, was that the congressmen and senators actually stay away from the selection process. They have staff who send out and recieve the nomination packets, and the nomination interviews are done by panels. Our son met the congressman the morning of his congressional interview only as a formality. The 12-member panel (yes, that was a bit many and a very tough interview!) were the ones to conduct the interview and rank the candidates. The senatorial interviews were similar, only neither senator was even present and the interview panels were smaller (no more than 3). So if someone was supposedly relying on connections in these cases, the only way a nomination would have been granted was if indeed the nominee was deserving.
Things have a way of working out, try not to sweat it all now. Just be humble and follow the process. If it is meant to be, it will happen!