Do you have limited slip rear end? I had this problem as you describe in an 05 HD with limited slip axle and it turned out to be lack of additive in the gear oil.
I do told last week by my local gm service manager that the limited slip axkes come from the factory with synthetic gear oil and also a certain additive in the LS axles. Could be the additive was never added? If your dealer can duplicate the vibration , Im sure they will figure out what it is. Good luck.