I’ve encountered this several times the last several years in my 07 LTZ. Similar to yours, it typically occurs when I’m slowing down at an intersection or coming to a stop. The truck will first throw a “Service Stabilitrak†warning, then when I accelerate out of the stop or intersection will shift out of the first gear with a an aggressive thunk. Once the shift occurs the warning goes away... until the next intersection or slowing.
Each time this has started happening I’ve checked the codes and gotten a “Fuel mixture too rich†warning. For me, I believe this is happening because I live on the US/Canada border and always go down to WA to get gas. But I tend to run the tank very low in between, causing the fuel/air calculation to get all messed up. Each time Ive had to go to the dealership and get them to reset it for a hundred bucks.
The big thing they always tell me is to ensure: A. Don’t run the tank into the empty light if avoidable, and B. Make sure you drive at least 11-12 miles straight after fueling to allow the computer to make new fuel/air calculations.
That’s my layman’s knowledge of what sounds like a similar problem. Hopefully it sheds some light on your problem. Good luck.