In case you're intrigued, it seems it may be the PSU. The issue only occurs with video cards using both 6pin pci-e power connectors. I have three cards to test with: a Radeon HD 4870 (2x 6-pin, issue occurred), a NVIDIA GTS 250 (2x 6-pin, issue occurred), and a second NVIDIA GTS 250 (1x 6-pin, issue did not occur).
I have had some nasty luck with PSUs. This will be my third one for this machine.