Since you have been buying "hand-tossed" style pizzas from Pizza Hut, they (Pizza Hut) would not be using a rolling pin. The dough balls are opened up and formed and stretched into skins entirely by hand. The problem with using a rolling pin is that it forces out most of the gases in the dough and will usually bake up with a flat and dense crust with poor oven spring. Also, if you roll the dough right out to the edge (to 14" in your case), you won't get a proper rim and the oven spring will be minimal. The only way to overcome this problem is to learn how to open up dough balls and form and stretch skins by hand. To make this exercise easier, I wouldn't let the dough balls temper for several hours after removing them from the refrigerator, as you apparently have been doing. That can make the dough balls much more extensible and hard to get a uniform skin thickness. I would cut the temper time down to about an hour or so.
Docking is not done right on the screen because that can cause the dough to be forced into the openings of the screen and get stuck to it. Docking is done on the work surface. Once the docked skin is formed to the correct size, it is lifted from the work surface onto the screen and dressed with the sauce, cheese and toppings.
The dough formulation you have been using has plenty of sugar in it so you should be able to get plenty of crust color. Pizza Hut uses a conveyor oven with a lot of top heat to produce good crust browning so adjustments may have to be made when using a home oven, such as lifting the pizza off of the screen toward the end of the bake onto the top oven rack position, where it can get more top heat to yield more top crust color. I don't have a gas oven, so there may be other kinds of adjustments to get the same results in your oven as I do in mine.
It sounds to me that what you need most to do at this point is to develop your dough handling skills and to learn how best to use your particular oven. We all go through this when learning to make pizzas.