Can't say that I've tried too often for last minute but when I have & it's not available I would do the DLR Hotels on points. (If you have purchased direct for usage of the Disney Collection.)
The month of Feb seems like a good off time to enjoy except for the Presidents weekend.
We just joined and I booked a few nights in feb. About a week ago. The whole month in a studio was not wide open but I had enough choices to make it a difficult decision for me