1992 Lincoln Town Car Transmission problem

I am having a problem with the tranny on this car. It had a Lincoln remanufactured tranny replaced at 98000 miles. About 3 months ago, it started slipping into neutral while driving down the road. If I moved the gearshift INTO neutral, and then back into drive, it would re-engage into overdrive. This occurred sporadically under light or no load, otherwise it shifted normally. About 2 months ago, it started not shifting into 3rd and 4th, even though the gearshift was in the overdrive position. I took it to tranny shop who found no error codes and suggested it be rebuilt. I took the car home until I could decide what to do about expensive rebuild in an old car.
Decided to take car to another tranny shop for 2nd opinion. They also found no codes, but asked them to drain and flush the tranny to see if that would help. They took off the pan and found no debris. They did find the dipstick cap in the pan, that Ford pushes into the pan on their new trannys. They also found no error codes. They said it needed to be rebuilt.
The car had started shifting normally again, so I drove it awhile. When first driven for the day, it shifted perfectly. If let sit for a couple of hours, then it would go back to the intermittently shifting into neutral again. It also started slipping a little on start out, but when I reached highway speed would work fine.
I then had a shop drain out two quarts of fluid and put in two quarts of Lucas Transmission treatment. After about 50 miles of driving it seemed like this was going to work, but then started the same thing over, meaning occasionally shifting into neutral at highway speed and occasionally slipping when first starting out. I discovered by trial and error, that if I put the gearshift in the Drive position and not overdrive, it would shift perfect all the way into 3rd gear. No slipping, no going into neutral, no nothing.
Although I know anything mechanical can fail, this tranny only has 20,000 miles on it and the type of problems it has are unlike anything I've encountered before. It's not like worn bands, etc. It almost seems like a linkage problem or possibly a valve problem but not a $1800 total rebuild problem. It also seems like the characteristics I describing should point to a specific problem that has happened many times over the years that Ford has made this tranny. Any help would be appreciated.
Rod