Larry would know what to do.
What, replace the platform, move to a Celeron and Z170 board, pick up a used HD7950?
It's actually worth considering a platform change, if OP values power consumption/heat/quietness. Skylake's iGPU is not even close to as fast as a 6790, but it's competent enough to at least
run modern games, and OP doesn't PC-game much anymore.
Personally, I'd just get a cheap 80/92/120mm fan and zip tie it to the video card, until I was ready to replace the whole thing.