OK today I ran the computer on its side, and I gave the card a nudge to make sure it wasn't keeping its old 'bent' shape (if it was bent), and rearranged the PCIe power cables. Then I played Crysis 2. Still crashed after an hour or so of gameplay.
Then I took it out. Placed it on a flat marble top, took the PCI bracket off, and tried to see any bending. I didn't see any bending, and the board was flat as far as I could see.
Then I took the stock cooler out (because it has a metal midframe that everything screws to), and put it on, screwing in each screw extra tight to make sure that the PCB followed the contour of the midframe (which should be flat). Then I plugged it in and played Crysis 2 again. It crashed within 10 minutes. I started the game again, crashed within 5 minutes. EDIT: just tried again, crashed within 10 minutes
Maybe if it was board flex, then my putting the original cooler on must have straightened out some curve ever so slightly on the PCB, exacerbating the problem. That's probably why it's crashing more quickly now.
Mothership: Thuban 1055T@3.7GHz, 12GB DDR3, M5A99X EVO, GTX470+Icy Vision Rev.2@840/3800, Vertex 2E 60GB
Supply ship: Sargas@2.8GHz, 12GB DDR3, M4A88TD-V EVO/USB3
Corsair: Macbook Air Ivy Bridge