Hi Beast 3,
1. I have a never-used, re-built differential with all new bearings & new bearing races; new pinion & new ring gear (3:27); accuarately adjusted with dial indicators, (no guess work by feel); & everything accurately measured with an inch-pound torque wrench; and filled with oil, installed in car & ready to go in a few weeks.
2. With 19" wheels, & 4-Ply Rated Good Year Safety Tread Tires, the radius from the center of the rear axle to the rubber tire tread near the ground is approximately 14-1/2".
3. With the rebuilt transmission placed in 3rd gear, the passenger side 19" rubber tire on ground, & rotating "only" the 19" driver's side rubber tire back & forth, this driver's side wheel backlash (measured with back & forth movement between both the Right & Left axles), & measured at the driver's side tire tread near ground = + 7/16".
4. With a backlash measured at 14.5" = 7/16" = 0.4375"; the rear axle nut is 5/8" = 0.625"; hence, calling the requested approximate backlash at the axle threads "X", (on the driver's side only), we can find "X" as follows: X / 0.625" = 0.4375" / 14.5" ; therefore X = approximately 0.01885".
5. Therefore if one measures the backlash for both axles on only the driver's side at the axle threads at approximately 0.01885", it appears the backlash for each individual axle measured at the threads would be approximately 0.01885" / 2 = 0.09425" for each individual axle.
6. I had a "well" used differential from the late 1940's or early 1950's on my 1930 Coupe that had an approximately 5/8" similarly measured backlash in lieu of the new differential's 7/16" backlash.
Hope this information is helpful.