Well, after all that work last year, I replaced the transmission AND GOT THE SAME RESULT.
I was pretty steamed. And deflated. So many hours and so much puzzling...
I saw a "small engine repair" sign in the neighborhood this week. Called the number and dropped off that day. Guy said he was a tech at a Honda shop somewhere. I explained the situation. He checked the performance and said "something's going on".
He took it to his shop for that reason. Called the next day.
Here's the major diagnosis.
THE FREAKING SPRING WAS WORN OUT!!! Man, I was NEVER going to get there!! Ugh... As tough as that SOB was to manipulate, I don't think that was on anybody's radar.
For some reason, he put on a new drive cable, even though it was a brand new drive cable. Like $65. For a cable... I know how these dealer guys are about OEM stuff. They'll spank you for going off the reservation.
So, apparently, the springs are good for 10+ years. $135 repair and in the end I'm just happy to have the mystery solved.
The mower is old enough to vote, so I shouldn't complain.
Thanks to all who assisted. Can't do it w/o you.