Hmm I know that FFXI had issues with DEP (Data Execution Prevention) you could try white listing the game. Details: http://i.imgur.com/9A7aK6n.jpg

That is really reaching into my bag of tricks without having you test every single compatibility mode. You could link and dump event logs and such and I could take a look at it.

I would suggest targetting this EXE but it won't hurt to add all of them since they are trusted apps. {DRIVE}:\{FF14 Install Location}\SquareEnix\FINAL FANTASY XIV - A Realm Reborn\game\ffxiv.exe

Also BSOD's on a Windows 7 machine make me immediately think of a hardware issue over software; more so if it's random in nature. I recommend running some sort of Burn-in test (Prime95 or Furmark) to stress your machine to show the leaks. If your machine crashes on those tests after about 45mins to an hour you have bigger issues.