Well, I was able to do some searching on the internet and I found the recipe for the Big Cheese pizza sauce and crust that I previously mentioned. In looking at it now, it may not be a close enough replication of the Godfather's pizza crust and sauce. As I said, the Big Cheese chain in my area was a knock-off of Godfather's, right down to the restaurants' layouts and video games, although we had both chains in the area and a few Godfather's still exist around here. I suspect a former Godfather's employee from Nebraska must have moved south and tried starting his/her own local chain in Kansas. http://www.recipelink.com/mf/31/8195
The measurements listed are in volumes, but you could try using the dough tools and coming up with weight measurements. Just as an eyeball guess, the hydration content looks somewhere between 60-65% for what the recipe calls for in water. I'm not a good judge on thickness, but again as a guess I would say it is somewhere between 0.1-0.15". The salt content seems somewhat lower than I would normally expect, but then it's been a while since I used this recipe. This recipe may not be close enough for you, and it does not go into the pans that are normally used (since Godfather's would be considered a pan pizza in my estimation and not a true deep-dish) or how those pans should be treated for baking. Just from memory, I would say you should use an all-purpose flour, like King Arthur's AP, but you might get some interesting and good results if you were to use a high-gluten flour.
If you decide to give this or any other recipe a shot, let us know how it turns out.