Does it have a full floater rear end? If so, I did not see it mentioned but did you have the axle hub(s) checked to make sure the lock nuts are tight on the hubs? Not the lug nuts on the wheels, but the nuts inside the hub that hold the hub onto the axle housing (you would need to pull axles to check). If these were loose the hub(s) would walk side to side when turning left/right. You would probably also have some fluid leaking from around the inner hub seals if this was the case though...
One other thing I have seen, you said the center bolt was replaced, was the corresponding "hole" in the cast axle perch ok? I have seen them rust/rot to the point where the bolt was sloppy in the hole and no longer aligned properly. However with the u-bolts tightened it would more than likely not have lateral movement, it would just not track straight.