See if you can measure the torque required to turn the pinion shaft now , then gradually tighten the nut , remeasuring the rotational pull until it produces the recomended restriction, I forget the # but it is only inch pounds on the bearing and will be in the shop manual, but many ft/lbs on the nut.
If that doesn't work for you , then you will just have to pull the diff apart and do the job properly.
