Back from camping... no idea this would be five pages. Thanks for all the advice, except from David, who seems the usual, low-T, knowitall who overcompensates because of tiny private parts.
To answer questions: filled tires, 3pt mower, bucket on front. Been on heavy farm equipment all my life. R1 tread.
Drove it to Deere, which is only 2 miles away. They shrugged their shoulders, said they could tear it all apart, but it would be a waste of time since the problem is so episodic. I might rig a lock/block like that on the 3pt hitch control, that when I'm in B it can't shift out. Normally it takes pressure, but there are times when in motion just a tiny touch of the finger can pop it into N.
I'm just going to keep it in 4wd all the time. Hate the extra wear, but when I want to stop, I want to stop.