Couldn't one consider BBQ pizza - which is quite common - a southern style pizza? Anyway, maybe I'm missing something, but other than Hawaiian pizza, I am not aware of any other American regional style pizzas . . . midwest style, or west coast style, etc. Sure, there is Chicago deep dish, and Detroit-style pan, etc. . . . but those names just refer to where they originated, not anything about the toppings or pizza itself which is specifically connected to the city/region like a beignet pizza or gumbo pizza would be associated with Louisiana. If place of origin alone is the standard, then one could consider the Magic Mushroom pizza to be a southern style pizza I guess. Maybe New Haven white clam pizza could be considered a regional style - but other than that and Hawaiian, I'm drawing a blank.
I like to make a psuedo-Rueben pizza at home. I use pastrami (> corned beef), mozzarella and swiss cheese, sauerkraut, and a brown mustard sauce in place of traditional tomato or white sauce. I think it's great, but not sure if it has a region . . .