## Not a fix - but a fix.
After trawling through other SE network sites, forums, newsgroups, and the like, I wondered if it might be related to mount order for local and remote file systems (there are a pair of CIFS shares mounted on this server, which each have subdirectories bind mounted elsewhere).
I pushed the CIFS shares higher in `/etc/fstab`, and moved all bind mounts to the bottom.
Then I rebooted.
Now `/run` aka `/var/run` is working as expected.
I don't _know_ that editing `/etc/fstab` mattered - but it's the only substantive change made that I know of.