If I remember correctly, MB differentials use a crush washer to set pinion clearance -- my 72 220D has the same problem, just worse.
I suspect that replacing this washer (it is really relatively soft hollow "donut" that can be complessed) will fix the excess backlash. The difficulty is getting the crush correct. The nut is tightened to get the correct rotating torque on the driveline, then straked in place.
Wear in the pinion bushing can allow it to move -- the crush washer is no longer "fat" enough to hold the pinoin gear in place.
1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!