DKM,
I have presented below my attempt at converting the Uno’s dough recipe to baker’s percent format. To do that, I first did some basic math conversions and then used the expanded dough calculating tool at
http://www.pizzamaking.com/expanded_calculator.html to come up with the final dough formulation in baker’s percent format. Since the flour is given as a volume measurement, I used the MassVolume Conversion Calculator at
http://foodsim.toastguard.com/ to convert the volume of flour to weight. For this purpose, I used the King Arthur allpurpose flour as a proxy for the (unspecified) allpurpose flour shown in the video. Since the flour in the video is shown in the measuring cups as being level, I used the Medium flour Measurement Method in the MassVolume Conversion Calculator on the assumption that the flour was scooped out of a container and then leveled off. For the water conversion, I assumed that a cup of water weighs 8.2 ounces. As the video notes, there may be a need to adjust the amounts of flour and water to achieve the desired consistency and pliability of the dough.
With respect to the flour, you will perhaps want to note that, according to the Uno’s website at
http://www.unos.com/nutrition.php, all of their deepdish pizzas use bleached flour. Whether that flour is an allpurpose flour or a cake flour, as has been discussed in the past, is not indicated in the ingredients list provided at the Uno’s website. Also, the Uno’s ingredients lists indicate that the flour mix includes soybean oil, quite likely in an encapsulated spray form, as well as more soybean oil at the time of preparation of the dough. It may well be that the added soybean oil is to oil the dough balls and/or the baking pan. For my purposes, I treated the corn oil and the olive oil separately in the dough formulation but, in practice, the two oils should eventually both be incorporated into the final dough. So, the total oil quantity in the dough from a baker's percent standpoint should be close to 20.24% (or maybe a bit less if all of the olive oil in the bowl does not get fully incorporated). Of course, one can choose to use soybean oil instead of the corn oil and olive oil shown in the video. For all practical purposes, the volume measurements if soybean oil is used exclusively would be about the same as shown in the dough formulation presented below.
I also learned from some Google searches that the two sizes of deepdish pizzas at Uno’s are 7” and 10”, not 12” as shown in the video. However, if the thickness factor is known for the 12” size, it should be easy to use that thickness factor to produce an amount of dough for any other size pizza, for both straightsided or slopingsided pans. To ascertain the thickness factor for the dough shell shown in the video, I used the deepdish dough calculating tool at
http://www.pizzamaking.com/dd_calculator.html. I simply used the baker’s percents from the expanded dough calculating tool and the pan shape and dimensions (12" and straightsided), together with the depth of the dough in the pan (1 1/2"), and played around with the value in the thickness factor box until I got the same weights as produced by the expanded dough calculating tool. In this case, the value of thickness factor I got was 0.13149. That is the value that one should use in the deepdish dough calculating tool for scaling purposes.
After all was said and done, I ended up with the following dough formulation:
AllPurpose Flour* (100%): Water (52.3182%): ADY (2.12676%): Salt (3.34964%): Olive Oil (4.04%): Corn Oil (16.2032%): Sugar (1.1963%): Total (179.2341%):
 333.26 g  11.76 oz  0.73 lbs 174.36 g  6.15 oz  0.38 lbs 7.09 g  0.25 oz  0.02 lbs  1.88 tsp  0.63 tbsp 11.16 g  0.39 oz  0.02 lbs  2 tsp  0.67 tbsp 13.46 g  0.47 oz  0.03 lbs  2.99 tsp  1 tbsp 54 g  1.9 oz  0.12 lbs  12 tsp  4 tbsp 3.99 g  0.14 oz  0.01 lbs  1 tsp  0.33 tbsp 597.32 g  21.07 oz  1.32 lbs  TF = N/A

Note: Nominal thickness factor for use in the deepdish dough calculating tool = 0.13149; no bowl residue compensation factor
*Based on King Arthur allpurpose flour
As a cross check of the above dough formulation against the real thing, I compared the pecking order of a pepperoni pizza using the above dough formulation against an Uno’s pepperoni deepdish pizza, and the numbers are in the right place in the pecking order. I should note, however, that Uno’s does not use a combination of provolone cheese and mozzarella cheese. According to their website, they use only lowmoisture, partskim mozzarella cheese. Also, they use a somewhat different pizza sauce. They use a combination of diced tomato and tomato puree, rather than ground tomatoes. The Uno’s sauce also includes salt, spice (quite possibly including oregano and basil), and black pepper.
When I have a chance, I would like to extrapolate from the 12” size pepperoni deepdish pizza to a 10” size to see if the proportions of the two size pizzas line up properly. To do this, I will have to calculate the amounts of cheeses and sauce used in the 12” size per square inch of surface area. However, for now, I think the above should get you started.
Peter