Most pizza places use their regular dough to make breadsticks. It would be far too complicated for most to make a separate breadstick dough, especially if it has to be done in the stores (and not from a commissary). They just roll the dough into a rectangular shape and cut into the desired number of breadsticks. In some cases, like Pizza Hut, a rectangular pan (I believe it is 8" x 12") is used for baking purposes. I have seen used PH breadstick pans on several occasions recently on eBay so you may be able to see what such a pan looks like. In PH's case, the dough is baked before cutting into individual breadsticks. I believe the dough is allowed to proof in the pan before baking. This gives the final breadsticks their rise and softness. I don't know which dough PH currently uses for breadsticks but it is possible that the dough comes into their stores frozen, as is the case with most if not all of PH's doughs at the store level. In other places, such as Papa John's, the dough is cut into breadstick pieces before baking. From photos I have seen, it looks like Domino's does it the same way as PJ's. PJ uses its regular dough for a 14" pizza to make breadsticks.
It is easy enough to take a pizza dough recipe and either use it as is or modify it for the number of breadsticks you want. For example, you might use 2 ounces of dough per breadstick. If you want to make really soft breadsticks, including soft garlic knots, you may have to modify the recipe to use more oil. Whichever method is used, the seasonings can be added before or after baking. Commercial pizza operators usually use a garlic butter made from garlic (in several possible forms) and margarine or a blend of butter and margarine. Seasonings tend to be oregano or an herb blend and grated cheese. Of course, for cinnamon sticks, cinnamon/sugar based seasonings will be used, possibly with an icing.
For your purposes, you may want to find a dough recipe that you like and use and either use it as is or modify it for your purposes. I know that you have been looking into Papa John's pizza dough and the Lehmann NY style dough as well. Either can be used to make breadsticks, and you should be able to use either the PH method of baking or the PJ/Domino's method of baking. I personally would decide on the recipe (one with baker's percents), the number of breadsticks I want, the weight of dough for each breadstick (e.g., 2 oz.), whether I want to add more oil to get soft and tender breadsticks or to make garlic knots, and use the Lehmann dough calculating tool at http://www.pizzamaking.com/dough_calculator.html
to come up with the required quantities of ingredients.
If you are interested, Tom Lehmann's favorite method of making breadsticks is described at http://thinktank.pmq.com/viewtopic.php?p=23090#23090
. You will also see other methods in the same thread from other PMQ Think Tank posters.