If I understand this thread, I must confess that I find it very disturbing that any SA would condition an offer of appointment (and limit its timing for acceptance) on a candidate's willingness to commit to a sport and make an immediate decision. I fully understand why this happens at civilian schools (limited scholarships, etc). However, this is a SA. EVERYONE is on "scholarship," and -- once you show up -- there is no way the SA can condition your staying or your "free" education on playing your sport. Quite a few highly recruited athletes at SAs end up quitting their sports for various reasons. Thus, every SA had better be taking candidates that it wants regardless of whether they play their sport.
It was my understanding that all candidates have until May 1 to make their decisions on a SA (at least that is the case for USNA). To condition a candidate's appointment on an immediate decision or "threaten" a candidate who doesn't decide immediately on something SO important is, IMHO, a disgrace.
I don't know which other SA is involved, but I can guess. And is sickens me. I can't say whether USNA does the above, but if it does, my view / reaction is exactly the same.
Finally, don't attend any SA that you don't 100% want to attend. I've written before of numerous time this has happened with my candidates. Not once has the candidate ended up loving a SA that he / she wasn't super excited about attending. Rather, they end up miserable and bitter.
So, for the OP, if you really want to attend the SA offering the limited time appointment, go there. But if you don't, hold out for USNA. If you have a principal appointment, you are extremely likely (not certain, but as close as you can get) to an appointment. Also, if you're that great of an athlete, you should be able to play your sport at USNA (unless it's not a D1 sport there).