What can I use to substitute Parmesean & Peccorino?

Im making stuffed mushrooms and the recipe calls for Parmesan and Peccorino both of which we're out of. We life 30 min from the store so I don't want to go just for cheese. I have provolone, swiss, gouda, mozzarella, and sharp cheddar. will any of these be sufficient enough to substitute?