After seeing the Mellow Mushroom YouTube videos at http://www.youtube.com/watch?v=P7-oxqmv7L8&feature=related,
I can see how there may be a similarity between the MM pizza and a Papa John's pizza.
Out of curiosity, I did some searching on what goes into a MM pizza dough. This is an old item, but in 2003, at http://www.vegfamily.com/forums/showthread.php?t=503&page=2,
there is a post by capersmama that the ingredients for a MM dough, as given by MM itself, are as follows:The ingredients include flour, salt, yeast, molasses and vegetable oil. In addition, our sauce does not contain any [animal products or byproducts] either--just tomatoes, spices and water.
Note: The bracketed entry is mine.
Of course, water is also an ingredient. I read in several places, including at the old MM website at http://mellowmushroom.com/public/old_site1/aboutus.html,
that the water is spring water (in many cases indicated to be Georgia spring water). Elsewhere, including at http://frenchtowner.com/travel/mellow-mushroom-pizza/,
I read that the flour is a high gluten flour that is vitamin enriched high gluten flour with wheat germ. There apparently is no refined white sugar used in the dough.
Things change, so it is possible that the ingredients for a MM dough have changed over time. However, I would say that using molasses and spring water (or possibly purified water using reverse osmosis) are staples of the MM dough. I did not read whether the molasses is in a liquid or dried form. In either event, the amount of molasses shouldn't be so great as to cause the bottom of the pizzas to darken prematurely when baked in a deck oven.
From the videos, I would say that high gluten flour is a distinct possibility. See, for example, http://www.thefamuanonline.com/2.10465/pizzeria-offers-healthy-options-1.1401434.
Sometime you might purchase a basic MM pizza, such as a 14" (medium) unsliced
pepperoni pizza, weigh the pizza (preferably in grams), and count the number of pepperoni slices. Or, you might just buy a basic cheese pizza. The weights might offer a clue as to how much dough to use to replicate the MM pizza. If you can provide the numbers, I might be able to suggest something. You might also send an email to MM and ask them if they have the Nutrition Facts for their pizzas. There is no need for you to explain why you would like that information. However, if you tell them that you have allergies or special dietary requirements (e.g., you are a vegetarian/vegan), they might also tell you what goes into their doughs if you ask for that information also. Although MM has no stores in California, you might also ask if the flour they used is bromated, which is a legitimate dietary/health concern given that California deems bromates to be carcinogenic.
EDIT (9/13/14): For the archived Wayback Machine version of the frenchtower article, see http://web.archive.org/web/20120724105956/http://frenchtowner.com/travel/mellow-mushroom-pizza/
: unfortunately, the vegfamily item was not archived at the Wayback Machine, but fortunately the pertinent portion is quoted above.