Preheat the oven to 400 degrees F. Bring a large pot of water to a boil, salt generously, and boil the pasta until al dente, tender but still slightly firm. Drain.
In a large bowl, toss the cooked pasta with the marinara sauce, 1/4 cup of the Parmesan, the pecorino, and the cubed mozzarella pieces. Season with the black pepper and red pepper to taste, and mix until well combined. Transfer the pasta to an oiled 9- x 13-inch baking dish. Cover the top of the pasta with the sliced mozzarella, and sprinkle with the remaining Parmesan. Bake until lightly browned and hot, about 30 minutes. Serve immediately.