Sounds like the backlash is not set quite right, or that the tooth contact pattern is off. Both are easy to check while the axle in the car UNLESS its an 8.75" axle. Since that is what you've got, you can take the center section out and check it without disassembling it. You'll need a dial indicator micrometer with a magnetic base. Set it up so the axis of the shaft is tangent to the gear rotation with the tip against one tooth on the ring gear. Gently rock the ring back and forth. You'll feel a small amount of free play where the ring moves without moving the pinion. That small amount is the backlash. Measure that and see if its in spec. (check for that, I don't have it handy right now.) If it is, take the micrometer off, and apply a small amount of white grease, OR , clean the ring gear and apply blue dye or permanent marker. run the ring gear a full rotation. Look for the bare metal on the teeth, it should be a nice contact patch centered on the tooth, not only side to side, but base to tip of tooth. If not, that is your problem.
