There are several places slop can develop in a rear end- - - -wear of the ring and pinion gears, bearings, looseness between the axle gears and spider gears, wear of the cross pin the spider gears run on, axle spline wear, etc. There are adjustments that can minimize slack between the gears, but when they are moved, the result is almost always a whine caused by interrupting the contact pattern between the gears that has established itself for decades of running in the same relationship. Axle gears, spider gears, pivot pin, and axle spline wear all require replacement of scarce, expensive parts. The best bet is to find a complete rear end to replace the sloppy one. 50-something years ago original equipment parts might have been available, but finding new individual parts now (other than bearings) would be difficult. Put an ad into the swap meet forum- - - -somebody probably has one in better condition than yours stashed away. Setting up a rear end properly was one of the most difficult skills I tried to teach- - - -it takes a huge amount of experience to do one right.
Jerry
