I don't mind Giordano's but it's not actually deep dish, it's a stuffed pizza. Stuffed pizzas have an extra layer of dough inside. I much prefer deep dish.
To me a "stuffed" pizza would be a calzone, or panzerotti....i.e. the extra layer of dough would be on top, and then sealed in.
If there's still toppings visible, then it isn't stuffed. The way you're describing it makes it sound like a double-decker pizza.
And you're right, it was doughy but I just assumed that's what a deep dish pizza would feature, since they're so goddamn big.