I finally got it fixed. For anyone else who is having a similarly mysterious issue, check Event Log. Not for hints as to why it's failing, but for hints that event log is *causing* the issue. That's right, event log *caused* the issue!
The thing to look for is any log folders in "Applications and Services\Microsoft\Windows" that have slashes in their name. This indicates that the registration for the provider for that event log is missing in the registry. In my case this was what I needed:
Windows Registry Editor Version 5.00
[HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\WINEVT\Publishers\{747ef6fd-e535-4d16-b510-42c90f6873a1}]
@="Microsoft-Windows-PrintService"
"ResourceFileName"=hex(2):25,00,53,00,79,00,73,00,74,00,65,00,6d,00,52,00,6f,\
00,6f,00,74,00,25,00,5c,00,73,00,79,00,73,00,74,00,65,00,6d,00,33,00,32,00,\
5c,00,6e,00,74,00,70,00,72,00,69,00,6e,00,74,00,2e,00,64,00,6c,00,6c,00,00,\
00
"MessageFileName"=hex(2):25,00,53,00,79,00,73,00,74,00,65,00,6d,00,52,00,6f,00,\
6f,00,74,00,25,00,5c,00,73,00,79,00,73,00,74,00,65,00,6d,00,33,00,32,00,5c,\
00,6e,00,74,00,70,00,72,00,69,00,6e,00,74,00,2e,00,64,00,6c,00,6c,00,00,00
"Enabled"=dword:00000001
(Note that the hex sections show up as text when viewed in regedit.)
In my case I just re-entered the data using regedit while looking at the data on a working system.
No idea how it got deleted in the first place, but re-adding seemed to do the trick.