I can't speak for the firms that do resume collect at WUSTL, but I wouldn't expect much out of a resume collect. My general perception of them is that firms only do it to be polite so they don't sour the relationship with the school career office. Even if they do plan on offering a few interviews out of a resume collect, they are probably only looking for really, really outstanding candidates. This is assuming they are in a position to hire at all.
I would follow M_Cools advice, but do targeted, tailored cover letters instead of mass mailing. Looking at your home state/city/region is always a good idea. Also, you should start networking with alums of your new school pronto.