I don't see much play in your U-joints or the flex discs. It could be that the parking pawl in your transmission is worn. Since you have the car on stands, there is no force against the wheels and or differential. Does the car roll a bit when you put it in park? Say more than 3 inches? Looks like 15 to 20 degrees play in the drive shaft.

With the brakes fully applied, do you notice any play when you shift from park to drive, to reverse? You would want to put your camera under the car when you do the test. Make sure there is a load on the differential so you know if the drive-train moves at the transmission or the diff.

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1991 F250 super-cab 7.3 IDI. (rebuilt by me) Banks Sidewinder turbo, hydroboost brakes, new IP and injectors.
2003 S430 - 107K
1983 300SD - Tanoshii - mostly restored ~400K+.
1983 300SD - Good interior. Engine finally tamed ~250K.
Monark Nozzle Install Video - http://tinyurl.com/ptd2tge