Update in case anyone is interested: I figured out what caused the problem. When I mounted the new drive I used to store my configurations onto Proxmox, I completely forgot to make the relevant /etc/fstab entry. The drive mounted successfully so I didn't realize at the time that I had forgotten to do that step. The update I ran from apt-get included a kernel update, so I restarted the machine to complete it. Since I hadn't modified fstab, my new drive was not mounted when the system started up again. Even though the drive wasn't mounted correctly, I still somehow had access to some incomplete version of the files in its directory (no idea how that works). So no fault of Docker, LXCs or Proxmox, purely PEBKAC.
Despite getting the files back I will still work towards a more resilient system and more regular backups.