Well, it's not a perfect solution, but when I run Crysis in windowed mode instead of fullscreen, it doesn't seem to crash. I played for an hour or so straight, and everything seemed to work.
I've loaded the new drivers, and still, if I try and run fullscreen, it crashes randomly after only a few minutes of play. Hell, it didn't even make it through the opening cutscene.
If anyone has any more ideas, I'm all ears.