One thing i did come across when i was fixing my truck was a shop called TCS transmissions .
One guy that worked there had a 2016 sierra 1500 same as mine and had the "shake" .
He said there were a couple parts in the transmission (6l80e) that were garbage and that they caused the vibration .
He reportedly replaced said parts rebuilt his trans and put in some upgraded parts and there was 0 shake after .