Okay, finally a breakthrough. The server hanged in the BIOS bootup screen.
My theory is that there is a problem with my hyperthreaded CPU cores 0-15. 16-31 are allocated to my VMs. The lower cores are used by docker and UNRAID. Disabling docker basically idles those cores since UNRAID doesn't use much CPU, which is why things are stable in that configuration.
I'm going to try disabling hyperthreading to see if that helps. I might have to replace the CPU. Or maybe the motherboard. Ugh.
Since my CPU temps never go above 41C even under load, I don't think it's overheating.
coppit's post in Server keeps hanging! was marked as the answer