I will leave to others to comment on the breadsticks part of your post since that is not one of my areas of expertise (at least not yet). So, I will limit my comments to the Papa John's part of your post.
I believe you are correct about the amount of sauce used at Papa John's for a 14" pizza. When I first started making PJ clone pizzas, I used about 5 ounces (by weight), based on a post by member dapizza at http://www.pizzamaking.com/forum/index.php/topic,994.msg38390/topicseen.html#msg38390
(Reply 14). However, I subsequently came to the conclusion that that was a bit on the low side--and that maybe 5 ounces was for a smaller pizza. The last PJ pizza clone I made used about 5.5 ounces of sauce. However, when I was last in a Papa John's store, it seemed that the workers were using a bit more, possibly 6 ounces, which would be a good round number when using a Spoodle. As you may know, Spoodles (a trademarked product) were invented at Domino's and are color coded. I believe the original Spoodles were/are made by The Vollrath Company. However, there are now quite a few cheap knockoffs made abroad, with different color coding. The "Spoodle" I saw looked to be black or some other dark color. For my next PJ pizza clone, I plan to use 6 ounces of sauce (by weight).
I have been working with only 14" PJ pepperoni pizza clones, but I think your dough weight for that size is on the low side. According to the nutrition information at Papa John's website, a 14" baked pepperoni pizza weighs 1024 grams (8 slices x 128 g./slice), or a bit over 36 ounces. It is hard to say what the pre-baked weight is, but for the PJ clones I have been making, the losses during baking have come to around 7-9%, based on a roughly 8-minute bake in my home oven, on a 14" screen, at the lowest oven rack position, at around 500 degrees F. For the amounts of sauce, cheese and pepperoni I have been using, I believe that the amount of dough for a 14" pizza is closer to 21 ounces, and maybe a bit more. I have also weighed baked pepperoni pizzas from Papa John's. I have discovered that there is a lot of variations in those weights because of differences attributable to the use of different workers (some have heavier hands than others), how busy they are, etc. For example, the last two Papa John's pepperoni pizzas I bought weighed about 37 ounces and 33 ounces. The 37-ounce pizza was made when things were slow; the 33-ounce pizza was made during a busy period with only one worker in the store for most of the time that I was in the store. My last PJ pepperoni pizza clone (baked) weighed a bit over 35 ounces. I used around 9 ounces of diced low-moisture, part-skim cheese.
I will have to try your suggestion to use a food processor to dice the cheese. I have been doing it by hand, which takes a lot of time to get a fine dice. I have tolerated this in the name of trying to replicate Papa John's pizzas.