As Randy has pointed out in another thread, his formulation for the American style produces a good-sized 16-inch pizza or two 12-inch pizzas that are a bit thinner than the 16-inch. Doing some rough calculations, I estimate that the dough for the 16-inch size weighs around 28 ounces. By my calculation, using the Lehmann/Ostrander thickness grading system, the thickness factor for Randy's 16-inch pizza is around 0.14. For each of the 12-inch pizzas (which use around 14 ounces of dough), the thickness factor is around 0.125. For comparison purposes, a thin-crust thickness under the Lehmann/Ostrander system is around 0.10 (e.g., a NY style), 0.11 (average, or medium) and 0.12-0.13 (thick).
I mention this since it is possible for you to use a thinner dough if you would like to have the crust thinner in the center without enlarging the rim to compensate. Since Randy's ingredient amounts are fairly easy to convert to baker's percents, it would be pretty straightforward to calculate the amount of dough (and ingredients) to use for any size pizza and any crust thickness you would like to try. If this is of interest to you, I can help you with the scaling of the recipe if you tell me what size and thickness you want to experiment with.