I just found this post and I'm in the same boat. I have a 14' Sierra Crew 4x4 Z71 with the 5.3 and have had the EXACT same problems that all of you have had, and I'm only on page 5 so far. I currently have just of 30k on the clock but have had this issue since about 11k. Had it in to my local dealer 5 times, including some work from outside of the dealer (thinking it was just an alignment or balancing issue), and they still can't get it right. They also told me that they weren't any ETB's from GM about any kind of vibration problem, which I now find hard to believe.
On Tuesday I'm heading out of town to the dealer in which I purchased the truck to have them work on it. My next step will be to consult an attorney about this. Like all of you, I paid over 50k for a truck that vibrates all over the place. About the only progress that I've made is that the service rep came to my home on a Saturday and drove the truck, and also felt the exact same thing that I've been complaining about. I highly doubt that they will do anything however.
I am completely fed up with this however. My wife Acadia doesn't do this, neither does my 64' Cadillac. I want it fixed.
Glad I found this site, and pissed I didn't look for it sooner.
Brandon