The parts needed can be broken down into two parts 1) the gasket set and 2) the pistons. The Dealer can order the gasket set right now. In order to order the correct pistons, the engine will need to be torn down and inspected to see which pistons are needed A,B or C sizes.Can they even order the parts without having my engine apart to see the piston size?
Can you get a conformation that they at least ordered the gasket set?
Then maybe you can push the Dealer to teardown the engine down and order the pistons. Yes, they will provide you with a rental car.