Always Check the Fans
Of course, I guessed it was the game and/or the new drivers that were doing it, especially since a lot of other people were reporting crash bugs. But I eventually figured out that the GPU was overheating. I have a XFX Geforce 7900 - and one of the ones that's pre-overclocked a bit on purchase - so I theorized that maybe it was just overclocked too far and spent too much time fiddling around with the clock settings. Still no luck.
In the end, I cracked the case and saw that the rear case fan wasn't actually turning. Well, that'd do it. I had checked previously and it was blowing air but I guess the fan was full of gunk and the rpm was down enough that the GPU was overheating. Weirdly enough, in a land of Microsoft tech junkies, I couldn't get a replacement 120mm fan in Redmond and ended up getting it via the magical power of the Internet.
So, the moral of the story - if you're having heat issues, always check the fans.