Folks…Well, I guess it was the battery (both of the batteries that I tried) after all.
Some time ago I ordered a second remote as a backup, which just now I opened and installed. It worked correctly.
Then to be complete I took the battery from the new remote and put it in the old remote, It also now works correctly.
My battery checker shows the old battery to be “good” (scale is from “poor”, “weak” and “good”) with a rating about 1/2 way between “weak” and “good”, closer to “good”. The battery from the new remote pegs out the “good” range.
When I put the old battery in the new remote, it works for a while and then starts triggering the “low battery” message.
So, thanks for you time and ideas - looks like I need a new battery tester…RDK