Ultimately the fix I found was similar to the one @Anthon posted.
I ended up making a directory (`VAR`) in `/home`. I copied the contents of `/var` into that, then changed `/etc/fstab` such that `/dev/md2` was being mounted at `/var`. Then I rebooted the system. When it came back I created a new `/home` directory (now ending up on `/dev/md1`), moved each of the user accounts (sitting in `/var`) into `/home`, and then moved the contents of (what is now) `/var/VAR` into `/var`. Then I restarted the machine to fix issues involving `/var/lock` and `/var/run` being messed up.
While this is very messy, it's the cleanest way I found to resolve the issue, as it avoided having to deal with symlinks and other messes in `/home`.