The short version is that I bent the PTO lever so it holds the coupler farther onto the driveshaft.
The long version is this:
I read all the posts on the PTO coupler and I never saw anything about bending the rod.
Maybe it's a common fix and I just missed it.
Inspecting and troubleshooting the PTO coupler through the trans filler hole I discovered:
The driveshaft teeth look ok.
When engaged the coupler had more than 1/2" of for/aft slop in it.
Only about 1/8" of the slop was from the inside lever to coupler.
The majority of the slop was from worn parts outside the case at the operators lever below the spring.
So I ordered a new assembly which includes both inside and outside levers for $35.
But, in the meantime I needed to mow the lawn so I did a temporary fix.
(In the following explanation, all directions are from the drivers seat)
I needed to take the slop out of the engaging levers and to keep the coupler farther forward on the driveshaft so it wouldn't disengage on it's own.
To keep the coupler farther forward on the shaft I needed to turn the outside end of the coupler lever counter-clockwise. But how? Tack welding it would be a pain to undue, bushings would be tedious and probably would not work.
So, 2" from the spring end of the rod/lever I put a 1/4" bend. I put it in my bench vice and tapped lightly with a hammer to get the 1/4" bend. And I punched a divot on the bend side of the handle so I would know which side went forward when I put it throught the collar and installed the cotter pin.
It worked. Engaged there is only 1/8" free movement and it stays farther onto the driveshaft.
I mowed the lawn without a peep from the PTO.
If everything inside the case is good then bending the rod is a quick and easy fix.
It may not be your cup of tea to do it this way but it works.