"It's not a true crash, in the sense that the bluescreen was initiated only because the combination of video driver
and video hardware was being unresponsive, and not because of any synchronous processing exception".
Since Vista, the "Timeout Detection and Recovery" (TDR) components of the OS video subsystem have been capable of doing some truly impressive things to try to recover from issues which would have caused earlier OSs like XP to crash.
As a last resort, the TDR subsystem sends the video driver a "please restart yourself now!" command and waits a few seconds.
If there's no response, the OS concludes that the video driver/hardware combo has truly collapsed in a heap, and it fires off that stop 0x116 BSOD.
If playing with video driver versions hasn't helped, make sure the box is not overheating.
Try removing a side panel and aiming a big mains fan straight at the motherboard and GPU.
Run it like that for a few hours or days - long enough to ascertain whether cooler temperatures make a difference.
If so, it might be as simple as dust buildup and subsequently inadequate cooling.
I would download cpu-z and gpu-z (both free) and keep an eye on the video temps CPUID - System & hardware benchmark, monitoring, reporting