Snowdy, I've visited difaras a few times in the past year and have made some observations. He has changed things over the years, so these are based on the latest version I have seen. The cheese he has been using lately differs between the sicilian and the round pizza. Round gets grande fresh mozzarella, grande dry mozzarella, and a generous sprinkle of grana padano. Square gets buffalo mozzarella, grande dry mozzarella and grana padano. Between the two I prefer the flavor of the cheese on the buffalo mozzarella pies.
Don't underestimate how much the shape of your cheese will effect the final product. If you want to be as close to dom as possible get a box grater and use the slicing side just like he does. A deli slice would be much larger and thinner than what dom is using.
Dom's oven is really hot, my guess is about 650. The cheese melted in an oven this hot tastes different. Higher temps favor buffalo mozzarella or fresh mozzarella, so you my prefer normal boring old dry cheese in a 550 degree oven.