What I don't get is why you're motorboating it at all, since you said you're using it for deep dish.
I understand your problem, but I don't know if I have an answer. I often wonder if places like Malnati's regularly end up with watery pizzas, because my deep dish does end up somewhat watery about half the time, and I'm still not sure if I consider that a bad thing. (I've had Malnati's once, but I didn't pay attention to whether it was at all watery.) I've tried adding Full Red Extra Heavy Tomato Puree to Saporito Filetto di Pomodoro, to thicken it, but I didn't like how the puree changed everything. Perhaps I should try it again, but with something more dense than puree.
I hate draining tomatoes for a few reasons: 1) I paid for that tomato juice; 2) Draining water = draining flavor; 3) If I need to process tomatoes in any way, I'm probably not starting with the right tomato product, because depending on what particular pizza style I make, there is most likely already some kind of tomato product that is processed exactly how I want it. (I'm a very big fan of 7/11/Tomato Magic for almost all pizza styles. I think it works great for deep dish at home, but it's nowhere near as chunky as Malnati's sauce, and I would want something chunkier if I was selling it.)
If I was producing deep dish at a high volume, I'd probably try using one can of unprocessed tomato strips per about every 2 or 3 cans of Tomato Magic, to get some big tomato chunks on the pizza without ending up with excessively chunky sauce. I don't know if that would be too watery.
One thing I will try whenever I make another deep dish pizza is baking at a lower temperature. I currently do deep dish at 450, but I've been thinking about going down to 425 because I think 450 is just a little too hot to end up with oozing cheese at the same time that the crust reaches its ideal degree of being done; at least with the portions I currently use (8.38 oz/238 g of cheese for 9"; 20.79 oz/589 g of cheese for 14"). I would think the longer bake time at a lower temperature might also help a little more of the water evaporate.
Another thing to consider is: Are you using too much sauce? Yes, deep dish is supposed to have a ton of sauce, but it seems to me that a lot of people use more than what is necessary. And that includes me. I use a hair more sauce than cheese on my deep dish pizzas, and I've recently concluded that I'm using too much. If I decrease the sauce portion a bit, there will still be plenty of sauce, but the pizzas will be less watery.