From what I have seen from Google Images, there are some Papa John's pizzas that can have enlarged rims that are of above average height but that is normally not the case. It could be that the top heat in the conveyor ovens that PJ uses could lead to an oversized rim but it is also possible that the rim was intentionally or inadvertently made larger by the worker in opening the dough ball to form the skin.
Since this thread is a PJ clone thread, I have tried to instruct members on how PJ makes its skins. Norma posted a video in Reply 679 at http://www.pizzamaking.com/forum/index.php?topic=6758.msg292489#msg292489
that does a nice job of showing how a skin is formed at her local PJ store. Later, in Reply 547 at http://www.pizzamaking.com/forum/index.php?topic=6758.msg325482#msg325482
, I posted additional material on this subject, including a video that shows everything in pretty much slow motion.
From your post, it wasn't clear whether your wife has been forming the skins with a rolling pin. If that is the case, the rolling pin will force a lot of the gas out of the skin and also leave the skin with a flattened rim. If she is to continue using a rolling pin, she could roll the skin to about two-thirds of the final size and open the skin the rest of the way out to full size by hand. This is a method that is often used to train beginning pizza makers until they get enough skill to open the skins up to full size entirely by hand. Tom Lehmann has discussed this method in a PMQ Think Tank post at http://thinktank.pmq.com/threads/hand-tossed-dough.6410/#post-41080
. But, whatever method you wife uses, it will help to make the rim larger at the outset.
I note also that you are baking on a stone. Sometimes it is possible to get a larger rim using a pizza stone by increasing the bake temperature, for example, to 525-550 degrees F, but the risk of the bottom crust burning or turning prematurely brown increases because of the large amount of sugar in the PJ clone dough as it caramelizes once the unbaked pizza hits the very hot stone. You could try a higher stone temperature as mentioned and, as soon as the rim puffs up, lower the oven temperature and slip a pizza screen under the pizza to keep the bottom crust from burning or turning prematurely brown. Another approach along the same lines would be to increase the hydration of the dough by a few to several percent. However, this will change the texture of the finished rim. Also, the dough will be wetter and may be harder to handle. But these are the kinds of changes you would have to consider. Simply baking a pizza longer will not achieve a larger rim. The final rim size is formed pretty much in the period right after loading the unbaked pizza onto the stone. I might add here that whatever approach you decide to use, you should let the stone preheat for about 45 minutes to an hour. Thirty minutes might not be long enough.
Please let me know what you decide to do and the results you achieve.