Ok, a follow-up. I was able to diagnose and fix the Q6600 rig, or at least I think I fixed it.
I hooked it up, it was still clocked at 3.6, and I ran GPU-Z, CoreTemp, and OCCT PSU test. Got a bluescreen a minute or two in.
So I took a look at the PSU, and it was really pretty caked-up with dust, so I suggested replacing it.
I removed the EarthWatts 650W, and installed a ThermalTake TR2 700W (BNIB, I had it on hand). It has a five-year warranty, so hopefully it doesn't fail before then.
I hooked everything back up, and no bluescreen, but OCCT exited, due to crossing the default 85C temp threshold on the CPU. So I boosted the temp threshold to 95C, and it exited again, and suddenly shut down. BIOS shutdown temp was set at 90C, there was no higher setting except "disabled".
Somewhere along the line, I also downclocked it to 3.33Ghz.
Anyways, even clocking down to 3.15Ghz, still at 1.33v, it was overheating in the OCCT test. However, when I originally tested the CPU, it was good for 3.3Ghz at stock volts. So I set it back to stock volts, at 3.15Ghz, and OCCT PSU test finally ran for like 12 minutes straight without a hiccup, max CPU core temp 83C (still a bit high, IMHO, for that clock and voltage, something around 1.2v). Max GPU temp was 78C, according to GPU-Z, so I figured that was OK.
So I packed it up and called it a success.