I agree with everything Randy has said. I have not personally tried using bread flour in Randy's recipe (thin version or otherwise), but I don't see any reason why it wouldn't work. I even made an all-purpose flour version (thin NY style) that turned out better than I expected. My first choice would be high-gluten flour, as Randy usually recommends, but I am happy to know that other flours will also do a good job. You can't do these kinds of things with most recipes.
I think you have to be a bit careful when following someone else's recipe or formulation. The last photo you referenced in your post is a 14-inch "thin" version of Randy's American pie that I made based on Randy's basic recipe. But, even there, I followed Randy's instructions as closely as I could, with essentially the only change being a shorter knead time because of a smaller dough ball size. To replicate Randy's results, I think it is important to use the proper oven temperature and, if possible, to use a pizza screen, as Randy recommends. While I haven't tried it yet, I am reasonably confident that you can make Randy's American style on a stone, but you may have to experiment with stone positioning and oven temperature and bake time to get the equivalent results. Using a pizza screen, I was able to avoid all of this experimentation. But, even if you use a stone, you have to be careful with the oven/stone temperature because Randy's recipe calls for a lot of sugar and honey, which can lead to premature or excessive browning of the bottom crust when the dough is in direct physical contact with a very hot stone. It is even possible for the crust to become browned before the rest of the pizza has finished baking. If I were using a stone, I would personally be inclined to still use a pizza screen (or a disk) to keep the dough elevated a bit above the stone. I would also use a slightly lower stone temperature just to be on the safe side.
I realize that you have been attempting a hand-kneaded version of Randy's recipe and that some changes may be necessary as a result. However, one of the things you may want to avoid is the temptation to add too much flour. Usually as you continue to knead a dough that seems too wet, some, or even all, of that wetness will disappear. If that fails, then you should add more flour sparingly, maybe a half-teaspoon or teaspoon at a time. I wouldn't worry too much about the window-pane test. I may be wrong on this, but I don't believe Randy has ever specified such a test for his American style. If you find that you are having difficulty hand kneading the dough, I would suggest, as I did in my last post in this thread, that you simply increase the rest period from 5 minutes to, say, 20 minutes. I have done this sort of thing with high-gluten flours and have found that it works wonders in hand kneading the dough. I think you will find that the total knead time will even be reduced. I don't know whether you will ever be able to exactly replicate the Papa John's style with your hand kneaded dough following the above suggestions, but I think you should get results that will satisfy you nonetheless.