I'm not sure why you believe that the cam is shot. If the shop where you had the cam install done is telling you this, RUN! find another shop. It should not be.
GM is not on the hook here, because belts are a wear item, and you have had the balancer off for the cam install.
A reputable shop should tell you "Get a new balancer (if necessary) , a new bolt (ARP crank bolt), new belts if they got chewed up, and reassemble. They may have to run a M16X2.0 tap to clear the first few threads. This does not sound difficult, nor expensive.
As far as a lawsuit, you can file in small claims court easily and cheaply, but you better have your documentation in order, and have exhausted all avenues with the install shop.