The rear end slack is adjustable via shims that position the pinion gear fore/aft. Pushing it backwards reduces the gear clearance on the angled teeth. But its not a job for the shade tree mechanic.

Its possible that the driveshaft could be fixed, but it's probably easier to find a junkyard set. Or possibly take it to a drivetrain shop and have them replace the offending ends with some standard sized modern replacements.