It was a bad stick of RAM.
In retrospect, a kinda “duh” moment. I mean, I had never before knew that bad RAM could make your PC just hard shutdown and (presumably) burn a graphics card. At the same time, I did get Furmark and a CPU tester to run for 15+ minutes using my 560ti card without a crash for a while there, with all temps being normal. Plus, I replaced the PSU and the PC booted up (before crashing later). All that was really left was a RAM issue.
I declined the $30 labor costs to install new RAM, but went ahead and spent $60ish to get the Microcenter guys to remove my liquid cooler on the CPU and install a mid-line fan. I’m a parsimonious miser for most things, but even I have my limits – possibly squirting liquid coolant all over my machine or having to disassemble my own rig to prevent that, is one of the lines.
As mentioned though, the 970 card is definitely still dead. I just submitted an RMA request and we’ll see what they say. It’s within the 2-year warranty period, but I’m a “worst-case scenario” kind of guy when it comes to corporations. I’m guessing this will be a 2-3 week process, at best.
In the meantime… well, WoW works perfectly fine with the 560ti. And isn’t crashing anymore. Which has allowed me to convert all but 100k or so of my in-game gold into $180 Blizzard credit.
So yeah. There’s that.