I'm familiar with the dealer in question, although I've never bought anything there. Have a Couple of friends who have done business there, one who had a complete debacle going on with service on an older 2500 pickup that was not under warranty. Dealer replaced several thousand dollars worth of parts, including transmission, to fix something that was a low cost item, ironically enough an item that my friend told them they should check when he first dropped it off.
Anyway, I'll be anxious to see how this works out for you. The garbage they tried to pull on you with the Michelins, and the GM telling you there's nothing else they can do......not good. Best of luck and I hope you get resolution ASAP or a new vehicle.