I hate to be the possible bearer of bad news.......
We had a handful of customers with the same trucks that were going through about a gallon of antifreeze every 3 -5'000 miles. Checked for head gaskets, intake gaskets etc. Did a block check to see if combustion gases were getting into the cooling system and nothing came up.
We had one of these customers who wanted a 6.0ltr installed into his truck for more power. We did it!
After the engine was out (to see if we could find the original problem) we took the valve covers off and found that the driver's side head had many cracks in it!
We told the other customers what we suspected was the problem and asked them if they wanted to investigate.....All of them had the same problem......All of them on the left side of the motor only. I dont know if it was just a coincidence???
We called the local GM dealer and asked if this was a problem.....OF COURSE THEY SAID NOOOOOO. We asked them for price and availability on parts to fix truck.
The parts guy said there was 2 in stock in Waco TX. and as he was looking at the computer screen it started to go into negative numbers. What does that tell ya???
I honestly hope this isnt your problem....but.......be forewarned