Are you sure it is excessive back lash?
There could be many areas of wear that would indicate slop between the pinion, and the wheels.
Some places that wear: differential gears, the cross that the differential gears ride on, axle splines, etc.
There should only be .006" back lash on the ring/pinion. On the GM 14-bolt you can take backlash out by adjusting the spanner nuts that screw into the sides of the housing. Problem with taking lash out of a used set of gears is the fact that the gears have already taken a set to the current backlash.
I have taken backlash out of used gears before without side effects, but you run the risk of making the gear set noisy by changing the mesh of used gears.