Back when I worked in a pizza place, we solved this same issue by just pushing the pie in further (for thin), or by yanking one back to the start after a couple

Back when I worked in a pizza place, we solved this same issue by just pushing the pie in further (for thin), or by yanking one back to the start after a couple minutes (for well-done requests). In the second scenario, prep guy would put an empty screen behind the pizza to reserve the space.