I, too, have a batch of dough working. I took the numbers I calculated for your dough the other day and scaled the proportions down to make just enough dough for a single 12-inch pizza with the same crust characteristics as yours (if my calculations were correct). I followed your instructions as exactly as I could, except that I used amounts of ingredients in about the middle of your dough weight range (based on the 5 1/4-5 1/2 cups flour range you use). For sugar, I used the 3 tablespoons benchmark. I had no problems making the dough at all, and the amounts of flour and water were just about perfect, without need to adjust either. And the dough came out a bit tacky as I had hoped.
It's been a long time since I last baked a 12-inch pizza directly on a stone. Since 16 inches is pretty much considered the standard for a NY street style, I have been making that size for a long time. And, to do so, I have been using a combination of a pizza screen and the stone. One of the things that concerns me with a dough with a lot of sugar in it, especially a dough that has not had several days of fermentation to use up a lot of the sugar, is that it is possible for the bottom of the crust to brown much faster, because of all the sugar, than the top. This can lead you to believe that the pizza is done when it really isn't. That is one of the reasons why the Lehmann dough does not include sugar in the basic formulation. The Lehmann recipe is intended for professional pizza makers who bake on deck ovens where high-sugar doughs are prone to browning too much and too fast on the bottom. To overcome this, some professionals dress their pizzas on screens or disks and place them right on the deck floor. The metal of the screens or disks places the pizza a fraction of an inch above the deck floor and serves as a barrier to reduce overbrowning of the bottom crust. The longer bake time also serves to make the crust crispier since there is more time to drive out moisture from the dough.
I have made high-sugar doughs, like Randy's American style, but they are dressed and baked entirely on screens without a stone. There is no searing effect of a very hot stone on the bottom of the crust, so the bottom bakes up very nicely, even with all the sugar, and without significant bottom crust browning.
Interestingly, professional deck ovens operate at temperatures lower than most people think. They typically run from 450 degrees F to around 500-525 degrees F, much like home ovens. Have you experienced any problems with overdarkening of the bottom crust with your pizzas? I know that some people actually like that effect. Or is your stone on the middle oven rack position?
I will have to watch the pizza carefully when I bake it tonight, just as you do to be sure that everything comes out OK. If necessary, I can always move the pizza off of the stone and put it on one of the upper oven racks if it browns too quickly on the bottom. This is all fairly new to me since I almost never use sugar in my standard doughs except for the Randy American style which, as mentioned above, I do not bake on a stone.