This is a hardware problem almost without doubt, most probably overheating: BSODs are very, VERY rarely caused by user-land software and while obviously device drivers are often to blame, in my experience this sort of 'many things failing at once, kinda' problem is likely to be down to software.

I know you said you 'cleaned it out' but that doesn't mean the gfx card (the most common culprit in this sort of problem) isn't to blame if the cooler isn't up to it.

Yes, I know you say it's only this game, many reports will include such a comment, however that doesn't mean it's the game's fault: FFXIV does drive gfx cards harder than, say WOW or LoTRO (in my personal experience) but ultimately a gfx card should be designed to handle sustained heavy loads.

CHeck your working temps, both CPU and GPU.