PizzaEater,
I converted your recipe to baker's percent format and used the expanded dough calculating tool at
http://www.pizzamaking.com/expanded_calculator.html to come up with the following dough formulation:
Flour (100%): Water (62.5%): IDY (1.5625%): Diamond Crystal Kosher Salt (2.24867%): Olive Oil (5.95237%): NonDiastatic Barley Malt Syrup (4.62962%): Total (176.89316%):
 453.6 g  16 oz  1 lbs 283.5 g  10 oz  0.63 lbs 7.09 g  0.25 oz  0.02 lbs  2.35 tsp  0.78 tbsp 10.2 g  0.36 oz  0.02 lbs  3 tsp  1 tbsp 27 g  0.95 oz  0.06 lbs  6 tsp  2 tbsp 21 g  0.74 oz  0.05 lbs  3 tsp  1 tbsp 802.39 g  28.3 oz  1.77 lbs  TF = N/A

Note: No bowl residue compensation
Using the above baker's percents to make an amount of dough for two 10" pizzas using a thickness factor of 0.103 yields the following:
Flour (100%): Water (62.5%): IDY (1.5625%): Diamond Crystal Kosher Salt (2.24867%): Olive Oil (5.95237%): NonDiastatic Barley Malt Syrup (4.62962%): Total (176.89316%): Single Ball:
 259.3 g  9.15 oz  0.57 lbs 162.06 g  5.72 oz  0.36 lbs 4.05 g  0.14 oz  0.01 lbs  1.35 tsp  0.45 tbsp 5.83 g  0.21 oz  0.01 lbs  1.71 tsp  0.57 tbsp 15.43 g  0.54 oz  0.03 lbs  3.43 tsp  1.14 tbsp 12 g  0.42 oz  0.03 lbs  1.71 tsp  0.57 tbsp 458.68 g  16.18 oz  1.01 lbs  TF = 0.103 229.34 g  8.09 oz  0.51 lbs

Note: Dough is for two 10" pizzas; thickness factor = 0.103; no bowl residue compensation
In either of the above cases, the "effective" hydration is equal to almost 69.5%. Unless one uses a considerable amount of bench flour, that is a high hydration value. It is also likely to be difficult to mix/knead a dough with that effective hydration value in a food processor.
I am not familiar with the Alton Brown dough recipe but if you want to modify it to make it easier to make the dough, I would shoot for an effective hydration of about 62% if you are using a bread flour. That means a combination of hydration (water) and oil that equals about 62%. You should be able to use the expanded dough calculating tool to apportion the water and oil based on what you think you would like to achieve in the way of final results. For example, you might decide that you would like to keep all of the formula oil in the dough. That would be offset by lowering the hydration percent while keeping the total at around 62%. That combination would yield a crust that is similar to a Papa John's crust but with a somewhat thinner crust. There are many other possible combinations that should work.
I might add that the amount of yeast (1.5625% IDY) seems like a lot if the dough is to be cold fermented. It would be considered high (about double) even for an emergency type dough that is to be made and used in a few hours. Not being familiar with the Alton Brown recipe, I can't comment further on what might be a proper amount of yeast to use for the type of results you would like to achieve while staying within the parameters of the Brown recipe. Too many changes and you may end up with a different recipe with different results.
Peter