SOLVED FOR ME: I have a 2014 Silverado 5.3L LTZ and I have the stupid shake issue like so many of you. Oddly enough, I also have weird shifting like clonks which the US class action lawsuit only mentions 8 speeds when i have a 6. I road forced balanced the wheels\Tires and I have 3 sets of wheels so I know the vibration was not caused by one set. I tried tightening the leaf springs and it reduced the vibration but made the ride stiffer at lower speed.
The solution for me was adding a AFM disabler from Range technology. The vibration is gone and the transmission shifting is now smooth. It's only been one day and I am so happy, that I wanted to share.
I do love the GMC Sierra AT4 with a 10sp but don't need the 6.2L so the rumors that 2020 Sierra\Silverado 5.3L will come with the 10sp is great.