First step would be to get the right pressure on the pinion bearings. There is a crush sleeve that has to be smashed some to get about 14 inch pounds of pressure when you turn the pinion gear( this is a slight drag, pinion should not just spin ). Before the differential goes in. Also there is a factory shim between the pinion gear and the bearing, Did you all put that in. This will cause noise also. because the pinion isn't close enough to the crown. After that is when start to adjust for back lash. And having no back lash will make the differential hum. Also eat it up real quick.
Adjustment to crown wheel and pinion has to be done after bearing replacement on the pinion and carrier. It is a method that unless you have done a lot of diff repairs will amount to a trial and error procedure to get it right. Fortunately any work shop manual that you can borrow will have the way to set up the diff and there will be photos and directions on which to move to get the setting right. It is important to get the reading right as correct gear mesh will ensure a long lasting quite diff operation.
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