While I was composing my post, I got ta thinkin' 'bout other things I might try, such as trashing various prefs, which I then did (after reboot, no change), but I had seen the FileSharing prefs and thought 'what if somehow FileSharing has gotten disabled on the office Mac?' and when I went to check, that was exactly what had happened!
Enabled FileSharing, and all is well on the BearFamily Network once again!
- Kbeartx