My first time making deep dish, I roasted my veggies on the oven first to lower their moisture for my stuffed pies. I took the hot veggies and transferred them straight to the pizzas and put them in the oven and pulled the pizzas when the crust was done, about 25 minutes. Recently, I had to make them in a rush and didn't have time to roast the toppings beforehand so they went in cold. My pizzas took nearly a full hour to cook! Part of that was definitely the added moisture (and therefore mass) but mostly, I think it was just all that cold food slowing the process.
Now I think that hot toppings are the way to go if you want tasty, properly cooked pies that come out of your oven fast. Does anyone else do this? Keep in mind this mostly applies to supreme style pizzas with lots of toppings, I still do things the normal way for plain cheese or other pies that are real light on the toppings.