By the way when you do look elsewhere consider this, if you don't have any references (they do that where you guys are, right?) they might be a little anal with the papers they require. I know cuz i had that problem (I'm in egypt i dunno if the same stuff applies in the states) when i was looking for an apartment, they'd ask for all sorts of weird stuff, my passport, university papers (well proof of me actually being in one, that is) and the like. I'd suggest if you get suspicious try saying you don't have what they require, like saying you don't have a credit card currently ( i don't know if that's possible there, but..) sometimes when you state that you can't do what ridiculous thing they required they just back off on that certain request (especially if it sounded silly at first).
Like i said, most people who rented me their apartments were like that at first.They might just be scared you'd turn out to be a killer or something :P .
Just something to keep in mind
Jam it back in, in the dark.