The best thing you can do is to frequently check back to the reservation site and look for sites that open up for 2 days because of cancellations. Grab them, and then cancel your previous reservation.
It will really be a matter of a luck of the draw, but things do open up. I've been in the same situation, and had it work out.
Worst case, you have to move. Checking in and out really isn't that much of a hassle most of the time.