Can you give a more technical summary of the crash? What does the blue screen say? It may seem like gibberish but there are technical details when you get the blue screen.
I know you probably can't make it happen right now, but when you can again, you should write down everything that seems relevant.
I once figured out from a blue screen error that my Video Card wasn't completely pushed into it's slots and locked into place. Causing to work 90% of the time, until I started stressing it. The technical information from the blue screen pointed me into the right direction.
I also have seen a problem where a stick of ram hadn't 'locked' into place causing an occasional blue screen and I was able to figure that out. At first glance you couldn't tell, but after reading up on the information the blue screen gave I was able to fix my father-in-law's computer. (His was the RAM problem)
Most of the time you can figure out from what is said on the blue screen, what is causing it to happen since FFXI is the only thing that is causing this. I might be able to help you if you can get that information the blue screen is giving you. And if you have FFXIV installed, that game is a beast when it comes to computer resources, you maybe able to reproduce the blue screen from that game to since it commands so many resources to run.
My brother's I7, he has 12 Gigs of RAM can't run 14 to its full potential because of his video card..he needs a lot larger video card. So you maybe able to reproduce the error from 14 or another game that demands resources.
And...not sure bout Windows 7, and I've not had a blue screen since I upgraded to Vista and built my computer, but when you restart it, do you get a 'Your computer has recovered from a serious error' message? XP would usually give you that when you would get this blue screen and restart the computer.
IF you can get the technical information..usually by clicking 'show more details' that can help lead you to a resolution to your problem.
I will watch this post and reply accordingly.
Also, you should just for the sake of elimination. Take your computer apart. Take out your Video card and put it back in, make sure it clicks in all the way. Do the same to your RAM just to eliminate that possibility completely. And clean it all while you are there.