Adjust oven rack to upper-middle position and heat oven to 450 degrees. Arrange salami on large plate lined with paper towels. Cover with 2 more paper towels and microwave until fat begins to render, about 1 min. Combine olives, red peppers, banana peppers, and garlic in bowl.
On lightly floured work surface, roll dough into 14 in round about 1/4 in thick. Layer half of the salami, turkey, provolone, and mozarella on half of dough round, leaving a 1 in border around edges. Spoon olive mixture over mozarella and layer with remaining meats and cheese. Brush edges of dough with water, fold over filling, and crimp to seal. Brush 1 Tbsp oil over rimmed baking sheet. Transfer calzone to prepared baking sheet and cut four 1 in slits on top of calzone. Brush with remaining oil and bake until golden brown,about 20 min.