Give us a little better description of the movement you are seeing. Is the axle shifting side to side (in the same direction as the axle shaft) or are you seeing a movement front to back (relative to the car).
And which part of the axle is moving oddly? The center portion of the shaft between the CV joints?
If you wanted to isolate the problem at minimum cost with a little labor, you could switch the axles and see if the movement goes with the axle or stays on the same side of the car.
I'm no expert, but I've replaced axle shafts with new units. No problems with new units at all, but they cost a lot.
1982 300D at 351K miles
1984 300SD at 217K miles
1987 300D at 370K miles