That recipe is amazing. You could have a much better pizza, if you were willing to start at least 2-3 hours before baking. Pete could probably point you to a same-day recipe somewhere on the forum. Just add a little more water for the whole wheat.
Otherwise, this is what I’d try, given the parameters of 1 cup each of WW and AP and 2.5 hours. This recipe is based on measuring the flour as follows: stir and fluff the flour in the bag; lift it with a spoon into a measuring cup; tap the cup once with the spoon; level with a straight edge.
a. Make a sponge as follows: Mix 1 tsp of instant dry yeast (like Rapid Rise) with the cup of whole wheat flour. Heat six fluid ounces of water to about 120°F. Mix the water and flour and set aside for an hour.
b. Stir in half tsp salt. Stir in a quarter cup of AP flour. Stir in 2 tsp oil. Continue stirring in AP flour until the dough starts to become stiff, then stir for a few minutes more. Turn out on board and knead in the remaining flour. Dough should be tacky. Cover dough and set at warm room temp for an hour.
c. Preheat oven to 550°F. If you’re using a solid, shiny-bottomed pan, don’t. Get a darkened pan with small holes. Go easy on the toppings, especially the center. Shape, top, and place in oven. After a minute, lower temp to 450°F. I’m guessing the pie will cook in about 8-9 minutes.