I'm not a world traveler, but I've often booked on Priceline late in the evening (I think you can book until 11PM).

I don't know how the availability algorithms work, but I have to guess that if a hotel participates with Priceline, they are not going to be stingy with availability at 9PM. While airlines will prefer to send seats out empty to preserve their revenue on other tickets, I doubt Marriott says "OMG, if we make cheap rooms available at 9PM at night on an opaque booking site, people won't book us earlier at full price."