Just to finish up this thread. Another website said I may or may not need the special tool, depending on the conditions of the receiving splines. They turned out to be in excellent shape, so no special tool needed. But, I did have to lower the shocks to get enough clearance (barely 1/2") to take the half-axles out of the hub splines. The new rubber rear mount for the differential had trouble lining up, so I had to lower the springs all the way, thus I had to re-compress them to re-install them and the shocks. An unexpected job, but not difficult.
Total R&R time for half-axles and differential, 6.5 hours. No more differential whining, no more wheel play, and the rear end never rode better! However, it did not remove the "thunking" at each gear shift and downshift, but thanks to a series of recent posts by AdamB, I realize that is most likely a vacuum problem, so I'll be overhauling my vacuum pump gaskets shortly, and tracking down any loose or open vacuum hoses/connections. This forum is a really positive resource for the DIY crowd!

SteveKaa

1982 300SD 300k