Preheat oven to 400 degrees. Squeeze moisture out of zucchini and mix with eggs and 2 cups of mozzarella cheese. Fill bottom of 9x12 cake pan with mixture and bake for 25 minutes. Remove from oven and spread with sauce, green peppers, mushrooms, onions and remaining cheeses. Sprinkle black pepper and dried oregano on top of cheese. Dribble olive oil over top and bake for 20-30 minutes. Do not let cheese get too brown.