IMHO you need to re-engineer your axle/brake system. If it were mine, I would pull the whole axle and start with FORD axle ends that would match the brakes that you are using. Have them welded (using a jig for straightness) onto your existing housing. Then I would use new axles with sealed FORD bearings and you would have no issue with axle end play. All you need is to have the axle shafts long enough to fully engage the side gears in the differential. Dr Diff can furnish the axles. This how I built the Dana 60 for the Ramcharger...I used a Dr. Diff 35 spline spool, Dutchman axles with FORD "Torino" big bearings (Same as F150) and the FORD racing 11" x 2.25" drum brakes (cheap, but effective)

Your '68 Charger won't know the difference between the tapered bearings (Chrysler) and FORD bearings and I will never tell anyone