It will be near impossible to get a lemon law buy back for burning oil.
Compression test probably won't tell anything but regardless it's oil going past the rings causing the problem on a 5.3.
A call to gm corporate is a waste of time,I've been down that road.

My advice is to go back to the dealership and be firm that something needs to be done and don't take no for an answer, but don't loose your temper and be respectful.
If the service department won't work with you tell them you need to speak with general manager or owner if possible.
No one wants their boss to know they can't keep a customer happy.
Trust me if a customer takes the a$$hole route they will be very unhelpful and make it as miserable as possible for you.
(Trust me on that I own a shop)