Damn, I'm spoiled with the premed commitee at my school, I guess. Getting my PIs to get all their letters to the right place, and the transcripts (which held up my AMCAS for a month--one school just didn't send them, even though they got my request) has been hell. Fortunately I'm not also applying for fellowships. I was so relieved when, after nearly a semester of prepping to app for fellowships and then a summer of thinking it over, I realized that I didn't really want to do what the Rhodes/Marshall/Fulbright/Churchill would give me, even if I was fortunate enough to win. I would say, though, if you "got roped into Rhodes nominations," that you might want to think about that more seriously before heading to the interviews, etc. associated with the fellowships (I don't know if those have already happened, though). If it's just for the name/resume building quality, do you really want to do it? And do you think they won't be able to tell that?
Anyway, good luck again, I'll be mailing out number 6 today. I've still got 1 non-AMCAS left, and then a bunch of secondaries/supplements. At least it's easier to decide where I really want to go--if I can't muster up the motivation to finish the application, I think that really tells me something.