RE: slate or granite source?
You might want to try a machining supply, but the granite with those dimensions are going to be about 10 inches thick.
You don't need that kind of precision to build a balsa model airplane. For a building surface that size a hollow core door will be plenty sturdy and precise, not to mention much lighter. You can go as cheap as a couple of saw horses for stands, or build an elaborate structure to hold the door. </p>