If you had the well known lifter/collapsed lifter issue, that issue is resolved by removing the heads, inspecting and repairing as needed the valve train, the pushrods, and the lifters; as well as the cam; if needed.
Sounds like that was accomplished -- that is an engine issue.
If that issue were still happening; you would notice it in idle (Transmission in park or neutral) and while driving (transmission in Drive or Reverse or any of the manual forward gears).
You describe an issue that only
manifests itself when you have the transfer case
set to "Auto" and you are moving.
Thus, the conclusion is you have a driveline issue.
What you don't mention is whether you have a 2 speed transfer case or a single speed (ie, do you have, 4High, and 2High, Auto4Lo, or do you only have 2High, Auto and 4 High?)
Regardless...if you can demo this issue to a competent
service advisor/tech, and demo that it goes away when in 2High, then that same competent
service tech should be able to diagnose.
Your powertrain (engine, transmission, transfer case) are covered under the powertrain warranty to 5yrs, 60k miles...so rest easy.
I can tell you, I have a Denali w/ the 2 speed transfer case, and I can hardly detect a difference in the vehicle between being in 2 High and Auto...and given the winter we have had, I have had it in Auto quite a bit. It's smooth as butter.
For some more details on how this transfer case works, suggest doing a little google search for GM Autotrak transfer case. Here is one article.
If you are curious as to the internal workings of 4 wheel drive auto and how it differs from full-time 4 wheel drive and AWD…
Net, you need to find a dealer who is willing to listen; tell them to drive a pickup or full size SUV from the lot and see if it does the same thing...it should not.
You could have issue w/ CV Joint, TransferCase, Hubs, Transmission (although I doubt it, since it doesn't do it in 2WD), Front Drive Axle, etc...
Stick to your guns, regardless of whether they say you should or should not be driving in Auto, the vehicle in Auto does not tend to bind up, make noises, etc.
If you put it in 4hi, and drive on dry pavement, you could get some of what you are saying <--- don't do this.