I have on 05 Avalanche Z-71 4wd that I experienced the popping noises at sharp slow speed turns etc. After several trips to the Dealer, a certified letter to GM and threats with a Lemon Law Attorney the Factory came up with a whole new set of Body Mounts that replaces the shims etc. This is supposed to be a brand new fix. So far that has finally solved the problem. But we will see, the rest of you may wish to look into this. They don't want to do it since it is an all day repair.
By the way I had the shims etc. previously installed and nothing worked til now, and they took all of those out when they installed the new mounts. I crawled under the vehcle upon getting it back to be sure that these are different and they are.
The new G.M. Part Is GM#15772884
Mc