What is "American Style" pizza? I mean, really? Do you mean like Dominos or Papa John's? I'd classify the CURRENT WDW pizza as most definitely "American Style"...somewhere in between thin crust and Chicago style, with a 'bread-y' crust (shell), thick cooked tomato sauce, and mozzarella cheese.
Every region of America has a different "style" of pizza. There is no "American" pizza. When you say that, I think: Dominos, Pizza Hut, Papa John's, etc...
You can get all those by calling from your hotel room and having it delivered!