I haven't had issues the past few times I have played the game. Here is what I have done:
  • I have rolled back the Nvidia driver to the version just before the current one.
  • I have underclocked my GPU.
  • I reapplied thermal paste on the GPU (mentioned in the original post).
  • I play the game after a clean boot. (mentioned in the original post).

I am unsure of whether my ability to play is because of one or a combination of these things, but so far I have not had the DirectX error occur. Hopefully this information can help anyone else that comes across this error.