I have been successfully making Papa John's original pizza clones but have became curious about wheat crusts. Without thinking too much into it, I simply used my usual recipe described by Pete-zza in Reply #2:
http://www.pizzamaking.com/forum/index.php/topic,6758.0.html and modified the flour component.
I made two 14" wheat doughs:
200.00 g King Arthur 100% Whole Wheat flour + 154.44 g Sam's Club White Bread Flour
154.44 g King Arthur 100% Whole Wheat flour + 200.00 g Sam's Club White Bread Flour
Flour (100%): 354.44 g | 12.5 oz | 0.78 lbs
Water (56.5%): 200.26 g | 7.06 oz | 0.44 lbs
IDY (0.14%): 0.5 g | 0.02 oz | 0 lbs | 0.16 tsp | 0.05 tbsp
Salt (1.75%): 6.2 g | 0.22 oz | 0.01 lbs | 1.11 tsp | 0.37 tbsp
Canola Oil (7.3%): 25.87 g | 0.91 oz | 0.06 lbs | 5.7 tsp | 1.9 tbsp
Sugar (4.8%): 17.01 g | 0.6 oz | 0.04 lbs | 4.27 tsp | 1.42 tbsp
Total (170.49%): 604.28 g | 21.31 oz | 1.33 lbs | TF = N/A
All ingredients were weighed out with a digital scale, because I really feel it's essential for reproducibility.
I followed Pete-zza's descriptive instructions as well. Briefly, water, salt, sugar, and oil were mixed. The flour was added in three installments and once mixed together for <30 s using the thin spinners, I switched to the kneading forks. After kneading for 2 min, I sprinkled the yeast on top, and kneaded for an additional 6 min. I slightly oiled the dough (~1/2 Tbsp ea.) and let sit in 1.5 qt bowls open for 15 min in the fridge. I then used plastic wrap to cover each ball with one pinky hole placed at the edge.
A 68 h cold ferment in the fridge gave a nice rise that I've seen with the original (all white) balls previously, although I noticed the top was quite dry and almost leather-like. I just ignored this, and dusted each ball using equal proportions of semolina flour and cheap all-purpose flour. They sat out for ~1.5 h before I spread them out on the same flour mixture.
After docking, I put on ea:
5 oz Pete-zza's PJ clone pizza sauce
11 oz Sam's Club (Stella) low moisture, part skim, pre-shredded Mozz cheese
8-9 Grape Tomatoes
4-5 Mushrooms
4 Black Olives
1/2 Red Pepper
After 10 min baking at 500F on 14" screens, immediately coming out of the oven, they looked quite watery (from the toppings, as I've previously observed with the white PJ clones). I let them sit for about 3-5 min so the juices were soaked up, presumably into the baked dough, and then sliced on perforated pans.
In terms of flavor, I could not distinguish between the two different ratios of wheat:white. The higher wheat did, however, have a slightly tougher bottom, but I didn't mind this at all. I suspect dropping a minute on the baking time in the future would eliminate this slight toughness. The edge crust in both cases was a bit dry, likely due to the low hydration. I simply used PJ's garlic sauce with them and they were still excellent

Overall, I am very happy with both recipes and probably would use the higher wheat:white simply because for nutrition.
In the future, I'd like to pick up a wheat dough from PJ's and compare its weight to the recipe above, perhaps to better estimate their hydration they use. I'm not sure if it's safe to assume the rest of the ingredients are of the same proportions as in the original white crust, but the overall flavor was excellent in both ratios, so I don't see a need to change it. I've never seen them make a wheat at PJ's but I think it's likely they use the same sauce as in the original, although I'll probably just ask the employee when I pick up a wheat dough ball. Comparing their wheat dough to mine with an adjusted hydration with only a cheese topping (same for both) I think will allow me to see just how close the two crusts' recipes are in terms of other ingredients and flavor.
These were a lot of fun to make, because I was already familiar with the PJ clone. I'd recommend it to anyone looking to switch it up from the original crust. An obvious draw to this approach is the ability to use the already-made PJ sauce and no additional ingredients would need to be purchased except a wheat flour. I'd suggest increasing the hydration a bit, but not sure how much. Perhaps someone else has recommendations on this?