Park to reverse, the transmission feels like to gets picked up and drops into place

It sounds like you have a bad transmission mount. The exhaust and the cross member will need to be removed to replace the mount. Here is a picture of the mount looking from under the vehicle.

Yes, that is the job of the transmission mount, to keep the transmission in place during these situations. The engine mounts should be inspected as well.

Is it the transmission moving or does it feel like the rear of the car is actually moving? When you replaced the transmission mount what did the cross member it mounts onto look like, solid and no rust and the chassis looks the same? Is there any clunking, squeaking or other noises when the car moves to indicate a failed U-Joint? Think you could take a video of the engine as it is shifted between those gears, it is possible it's a failed engine mount if it is the transmission moving a lot.

Okay, in that case I would check the U-Joints, it sounds like at least one is binding very hard. I generally like to replace both of them if I have the pull the driveshaft, they both have seen the same amount of wear and tear, and it's easy to do while you have the shaft out anyway.

The part that goes into the transmission is the front slip yoke. It should be able to slip in and out but you shouldn't be able to move it up and down or side to side more than a tiny amount.
https://www.2carpros.com/articles/how-to-remove-a-drive-shaft
https://www.2carpros.com/articles/how-u-joints-work

No play doesn't mean one isn't damaged and causing problems. I've seen them look great from the outside and still be bad. You should be able to feel it though once you pull the rear yoke free. Try to move the joint in both directions, the bearing caps should move smooth and free.

Have you had any success or found a problem? Or just not had any time, I know how that is.

No problem. These days the time seems to get used up fast.

A slight clunk is usually play in the splines. I don't like to see any because it means the splines are very worn. The clunk is from the slack from the wear letting things move.

The A Arm broken free would make things interesting.

It can be repaired, how expensive depends on where the wear really is. If it is the splines in the front yoke then it's a simple thing to get a new yoke and change out the U-joint and yoke. I suspect it's a combination of wear in the yoke and the output shaft in the transmission. That will cost more but the only way to know is to check the various parts for wear. There needs to be some clearance in all of the parts or they will bind up but not an excess amount. To check it you would pull the drive shaft after checking the U joints for play, then you take the front yoke off and examine it and the output shaft for wear. The problem there is that without a known good part or a tester for them it isn't easy to tell if they are OK or not. I would see if you can find a transmission shop and have them look it over, they can tell you if it's excessive wear and usually have ways to test the parts.