I worked at the Homewood Aurellio's for a good year just after High School in the early 90's. It is a bit fuzzy now, but I will share what I remember.
The Cheese is a 50/50 blend of Chelino Scamorza and mozzarella. one of my first duties there was to cut the blocks into strips to be fed into the grinder. In fact, I have a nice 2 inch scar on my wrist from slipping with the knife while cutting the cheese. It was my second day on the job. 7 stitches.
I have seen some discussion over Parmesan. They use parm and oregano to top their deep dish pizzas after coming out of the oven.
The sauce came in a bag. It is made offsite. The thick crust and stuffed pizza sauce is different than the thin sauce. The sauce for the thick/stuffed is the same as their pasta sauce. It is a little bit thick and chunky. The thin sauce is a puree.
The crust was made and rested in the refrigerator. I honestly am not sure for how long, but it was a minimum 24 hours. I was not there long enough to know this recipe to my dismay. I do remember that they oil the outer edge of the pan before placing the dough in. It is not docked.
The thin pizzas are cooked on a conveyor system unless you request it goes in to one of the "old ovens". Which I recommend if they are not too busy. Homewood location only.
I also remember they experimented about once a month with their recipe. On a slow night, about once a month, the managers would make around 10 different pizzas all with little changes to them and taste test them. Therefore I believe it might have slowly changed over the years. Alternately, they were just bored. I dunno.
I hope this helps in some way on your quests for making this wonderful pie.