So after getting mucho annoyed with my laptop, I filed a bug on freedesktop.org, enlisting the help of the amazing Alan Hourihane to solve my problem. After some back and forth and trying of new drivers, we decided it was probably a hardware issue. He suggested something that had never occurred to me: swapping the RAM sticks around.
I did so, and my laptop hasn’t crashed since.
This was a very weird problem, since normally RAM errors cause problems all over the OS, like crashing programs and weird segfaults (unlike on windows, on linux you can assume extreme crashing is a hardware problem). But in my case it was always the same video crash. This is probably because on my laptop the video card actually uses system RAM to store data. There might have been a slight incompatibility in the way my RAM was installed, but it only showed up in this reserved section. I ran memtest86 and never found anything, so I had thought RAM couldn’t be the problem.
It just goes to show, big huge crashes are almost always RAM, even when you think they aren’t.