After updating BIOS, updating chipset drivers, clean installing NVIDA drivers, running CCleaner on the registry, reinstalling FFXIV to the same drive as Steam, and disabling fullscreen optimizations, I seem to mostly not be crashing.
I haven't tried to run the game for an extended period of time where it's the only program running but I'll give it a shot.
Heat hasn't been a problem, everything is operating at normal temperatures.

I did have my computer sort of lock up on trying to close another program while 14 was active which leads me to believe it could be related to other software or hardware. Running Windows Memory Diagnostic didn't result in any issues being found though. And I'm not overclocking or anything.