You are well equipped to make a Randy American style or a thin version of it as described in this thread. I have not yet tried using bread flour in that style but Randy did post a bread flour version of his recipe at http://www.pizzamaking.com/forum/index.php/topic,1698.msg15290.html#msg15290
(Reply 19). I also have not used hand kneading with Randy’s recipe but my recollection is that others on the forum have done so. I see no reason why you can’t either.
A good way to learn about pizza making is to try different versions of a recipe. For example, I first started with Randy’s basic recipe and gradually modified it to make thinner versions. Along the way, I experimented with reducing the quantities of several of the ingredients to see whether doing so would still produce a decent product (it did). If you like a Papa John’s style, I understand that Randy’s original recipe comes quite close. If you prefer a thinner style—an almost NY style--then a thin version works very well.
As far as the dough preparation is concerned, I don’t think it really matters which flour you use or which version of Randy's recipe you use. Depending on the flour you decide to use you may have to adjust the amount of water (hydration), and you may have to tweak the flour and water to get the desired finished dough condition, but the basic processing steps should be pretty much the same. If you decide to use high-gluten flour, it will be harder to hand knead such a dough, but if you introduce one or more rest periods during the mixing/kneading process, you should be able to manage it.
In your case, I would recommend that you make enough dough for a 16” pizza which, as you correctly noted, translates into enough dough for two, roughly 12” pizzas. There are several possible ways to use hand kneading with the different versions of Randy’s recipe, but I think I would use the following one.
I would start by dispersing the yeast (IDY) in with the flour. Then put the water and salt into a bowl and stir for about 30 seconds or so to fully dissolve the salt. Next, add the honey and sugar to the water/salt mixture in the bowl. To help dissolve the honey and sugar in the water, you can warm up a small amount of the formula water and mix the honey and sugar into it before adding it to your bowl with the rest of the water (which can be at room temperature or even cool). Next, gradually add the flour/yeast mixture to the bowl, about a tablespoon or two at a time, and mix in after each addition with a large sturdy mixing spoon. This is to better hydrate the flour without developing its gluten. Continue to do this until about 2/3 of the flour/yeast mixture has been added to the bowl. Then let the mixture rest for about 5-10 minutes. This rest period will be especially useful if you decide to use high-gluten flour, which yields a more extensive and elastic gluten network, and will allow the dough to soften and become more manageable. It should also help produce a more open and airy crumb in the finished crust, which appears to be a feature you like.
At the end of the rest period, I would add the oil. Normally, I add the oil at the very end before the final knead so that it doesn’t impede the hydration of the flour, but since you will be hand kneading I would add it to the dough mixture while it is still wet and easy to incorporate (as another option, you can even add the salt at this time rather than at the beginning). Once the oil has been incorporated, remove the dough from the bowl and put it onto a work surface. Mix/knead in the remaining flour/yeast mixture a little at a time. If the dough is too wet to handle and overly sticks to your fingers, you can use a bench knife to manipulate the dough by turning the dough as you gradually add more flour (I usually sprinkle the flour onto the dough). There is a natural tendency to want to add more flour, so you should resist doing so since this can lead to a dough that is too stiff.
Continue to add the flour a bit at a time and knead the dough until it become smooth with few surface irregularities. Ideally, it should be on the tacky side. If the dough is too hard to knead, as can happen with a high-gluten flour, let it rest for about 5 minutes, and resume kneading. Since you will be using volume measurements, it may be necessary to add more or less flour and/or water to get the desired finished dough condition. If such modifications are necessary, do so a teaspoon or so at a time. It is hard to say how long you should knead the dough, but you don’t want to overdo it. It is better to slightly underknead it than overknead it.
At this point, the dough can be shaped into a ball or disk shape, lightly oiled, and placed into a suitable container and then into the refrigerator. You should follow the remaining steps as outlined in the particular dough recipe you decide to use. One of the nice things about Randy’s American style dough is that it can be baked entirely on a pizza screen, using a short oven preheat (about 10-15 minutes). Every pizza I have made following Randy’s recipe and my variations of it have turned out very well. I hope you experience the same results.