Well, can close the lid on this for sure now. For future reference to people experiencing similar troubles, I found that one of my sticks of RAM was faulty. Since removing it, the game has been running well, and the troubles I've had with other games have too ceased. I was able to discover this by running the RAM-based torture tests of Prime95; Within minutes they would terminate with rounding errors. After testing my sticks individually, I found that one was defective, even though Memtest claimed it was fine.

Has any progress been made in diagnosing what caused these?

The text file is in the original attachment. Can you clarify at all on how they're 'random'? Have you ever seen crashes like that happen before?

The DXDIAG report is included in the rar that was attached. I could not upload the included mdmp files here because they were too large (10+MB each).

The full dump files (including the mdmps) are here:
https://www.dropbox.com/s/lig2rjc1nq94m49/Report.rar