So, I haven't had any issues for a bit now; and at least, not a single DX11 crash since 6.01. The only two changes I made were as follows:

I moved FFXIV off of any SSD and onto my HDD, and I'm not using any of the nVidia shaders anymore. Compounded with all the other changes most people have generally made, these at least seem to have resolved my issue. But make no mistake -- it's completely insane that I and any of you have to go through this amount of troubleshooting to fix an issue that should be fixed by SE. No game should ask you to reinstall Windows to work properly. :/