[James]

In my opinion the slip joint is worn out.

The ring and pinion will need further investigation (that's too much play). With a clean pan drain the oil out of the differential, then check it with a magnetic (should be almost no metal). Opening the cover on the differential. Look at the wear pattern on the ring gear. Compare that to the service manual picture, should be wearing in the center of the tooth on both side. You could also remove the drive shaft and the axles (this would unload the ring and pinion). Then rotate the yoke on the differential, should be very smooth operation. Depending on the ring and pinion wear and how much metal is in the oil, you might only have to readjust the backlash or at worst replace the ring and pinion with new bearings and seals.