Patrick - thank you very much for your response. I've enabled Driver Verifier on the machine. I have seen a couple more blue screens since then, but the bug check messages have been as all over the place as previously. I haven't seen any VERIFIER strings so far, nor any of the messages listed in KB244617 (it's been mostly SYSTEM_SERVICE_EXCEPTION so far). I will leave Driver Verifier enabled for a day as instructed.
Could you make any suggestions about where the hardware fault may be? My gut says the processor is the likely culprit, as it's the only piece I haven't owned and used before...but I don't know where to look to back that up. I've run one pass of memtest without anything coming up, but I'll run several passes after the Driver Verifier trial.