Papa John's does not publicly disclose the ingredients used to make its doughs and pizzas. However, when I was researching the Papa John's original pizzas, I found the ingredients list for PJ's thin crust pizza at a website of a company called Joy Foods Inc. That website is no longer around, at least under that name (the domain is for sale), but I was able to find the ingredients list through the Google cache feature. Here is the relevant information in relation to a pepperoni thin crust pizza:INGREDIENTS:
PAPA JOHN'S BLEND OF MOZZARELLA CHEESE, MODIFIED FOOD STARCH, WHEY PROTEIN CONCENTRATE AND SODIUM CITRATE: Part-skim mozzarella cheese (pasteurized milk, cultures, salt, enzymes), modified food starch, powdered cellulose (added to prevent caking), whey protein concentrate, sodium citrate, sodium propionate (added as a preservative)
PAPA JOHN'S THIN CRUST: Unbleached flour (wheat flour, malted barley flour), water, soybean oil, yeast, salt, natural and artificial flavors (milk), dextrose, calcium propionate (preservative), soy lecithin PAPA JOHN'S FULLY SEASONED PIZZA SAUCE: Vine-ripened fresh tomatoes, sunflower seed oil, sugar, salt, dehydrated garlic, extra virgin olive oil, spices, citric acid
PAPA JOHN'S PEPPERONI: Pork and beef, salt, natural flavors, dextrose, lactic acid starter culture, oleoresin on paprika, natural hickory smoke flavor, sodium nitrite, BHA, BHT, citric acid CONTAINS: WHEAT, MILK, SOY
To the best of my knowledge, Papa John's does not make the thin crust pizzas but they are delivered to PJ stores from the PJ commissaries. I believe that that particular pizza style was outsourced to another company. You can see the nutrition information, including weight information, for a 14" pepperoni thin crust pizza at http://www.papajohns.com/menu/popup_pepperoni.shtm#thin.
I have not tried to reverse engineer or clone the PJ thin crust pizza, and have no plans to do so, but if you compare the ingredients list with the DKM cracker style dough ingredients, you will see a similarity, with the main differences apparently being that the PJ dough does not include any sugar and it looks like it contains milk in some form.
I think I would start with a modification of DKM's cracker style dough but leave out the sugar and add either add some dry milk powder (which is what PJ's supplier most likely uses) or replace part of the formula water with fresh milk in some form.
Edit (3/28/14): For an alternative to the above inoperative link, see http://www.hpisd.org/portals/0/docs/foodservice/pdfs/Entrees/CafePizzaPappaJohns_Cheese.pdf