I managed to get a couple more apartment applications in last week, and found one place that said "ok, if you can pay rent up front for the summer, we'll call it a deal." I'd already put a deposit down on that place, so the amount I had yet to pay was doable. Five minutes and one check later, I had keys to a new apartment.
I'm not homeless for the moment, although the task now becomes finding a place to live once my lease here is up-- just under three months from now.
So stay tuned.