Uh-oh, the ambient temps barely went up and sometimes the system wouldn't boot.
I verified the BIOS I flashed the card with and noticed 2 differences from the original BIOS:
-- Voltage is 1.4V (1.3V in the original)
-- Memory config is slightly different.
I took my BIOS backup, created a 1.4V version using NIBITOR:
and flashed the card with that BIOS mod. I turned off the case fans to make the case even hotter (to stress-test the modded BIOS). The system would boot up normally AND the graphics wouldn't get corrupted when coming back from sleep mode.
So it seems that all that was needed was 1.4V (an not a whole new BIOS).