Mail, Automation can't be configured after Time Machine restore after OS re-install
Ugh. I never did figure out what went wrong. I re-formatted the disk (always a teeth-clenching experience), and re-installed Mojave from the thumb drive installer I made from the DosDude instructions.
So far, this is the same as before. But this time, when it was done installing and booted up, I used Migration Assistant to restore everything except my home directory, instead of everything.
Then, I logged in, and re-ran Migration Assistant, this time, restoring only my home directory.
Now, things seem to be working normally.