I tried switching to the iterative solver, and that does save quite a bit of RAM (as much as 400 GB), however the same problem still happens with somewhat finner meshes. It moves the bar up somewhat, but not enough. I have included the profile data from two different types of crashes. The first from before we switched to the iterative solver, and the second from after. Immediately below is the example of a crash using the direct solver. Note that it says "Out of RAM", but our actual ram limit was 1.97 TB, which is much higher than the 1.58 TB it lists using at the time of crashing. It is also important to note that simulations like this intermittently succeed with significantly less RAM than our limit (1.3-1.5 TB).
The next image shows a crash that happened after switching to the iterative solver. The profile shows almost no useful information:
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