Here’s my original request for help: Song ID help requested, no imagination necessary - Cafe Society - Straight Dope Message Board
Don’t bother trying to follow the link in the OP, the host site took the song down.
Anyway, for the follow-up: a friend passed a copy of my mystery song on to a friend of hers, and lo and behold, he came up with something.
George Benson’s “Doobie, Doobie Blues” from Talkin’ Verve (1968).
It’s definitely the same song, but it’s not an exact match. Benson’s “Doobie, Doobie Blues” has a pronounced melodic scat element (literally, “doobie-doobie-doo”) which my target song does not have. My target song has a pronounced piano element that Benson’s “Doobie, Doobie Blues” does not have. Aside from that, though, the tracks are identical within the limits of my hearing and memory. Guitar and bass parts seem completely identical.
So, I guess I’m wondering if there are any George Benson experts/aficionados in the house who might know of him having re-mixed “Doobie, Doobie Blues” on a later album? I see it as a track on several later albums, but I’m not familiar with his work outside of his hits, really.