I just installed the new heatsinks with some Arctic Silver Ceramique and the system's working... for now. The GPU heatsink seems to get hotter than the other one, which I guess means more heat away from the chip so that's good.
Posted too soon. The problem definitely seems to be the GPU overheating as nothing else in the system (except CPU) is warm but the CPU contigency isn't going into effect (faster fan speed and then 2 red lights). Maybe if I could lock the fan at CPU overheat speed it'd keep the GPU cool.