My bet is an early suregrip unit with 2 piece side gears and the axle is only in far enough to get the clutch plate, but not the gear that engages the spider/ pinion gears. It happens a lot at chassis shops that do not know danas are offset, they measure the short side and order axles, exact symptoms you describe. Late clutch type diffs had one piece side gears so they could "slide" by with that kinda work. I did a trans for a guy, car would not move on the ground after narrowing the rear, of course blamed the trans, nope, one axle too short, by a bigshot chassis shop.