Well, everyone, it appears I have finally found the problem.
It appears Dom2 did not like the way memory timing was set up in the bios. When I set all three memory parameters to 3 (two were set to 2), no lock ups. I ran battle replay about a dozen times without a single lock up. Before, the most I got was three in a row without a lock up, and the vast majority of the time it always locked up during each replay.