I was just made aware that I didn't follow up on this thread with a solution.
So I narrowed down the issue to Docker. Specifically, when dockers are restarted (instead of shutdown and started back up) there appears to be a memory leak related to system resource allocation. There's some set memory pool that gets consistently used up when a docker restarts until there's none left. At that point, unRAID goes haywire.
Storage devices can't be accessed (including the USB unRAID device), WebUI may fail to load, SSH won't connect reliably etc
Stopping the docker that you've restarted multiple times releases these resources back to the system and everything instantly begins working again. Since learning of this, I changed how I interact with my dockers so they aren't restarted but are completely stopped then started and I've experienced no more problems since then.