I am confident that your problem was not the King Arthur bread flour or the yeast per se.
The Lehmann dough recipe you mentioned was one of the first I modified for home use. It has since been modified to use a lower hydration percent (a bit less water) and a lot less yeast. But the recipe was not the problem, even when you added sugar to it. I think the problem arose from the amount of sugar you used and the way you used it in relation to the yeast. There may well have been other problems, such as the way you formed the skin for your 10-inch pizza (discussed below), but I think the sugar problem may have been the principal one from what you have reported.
If you indeed did use 1 1/2 tablespoons of sugar, that amount came to 5.4% by weight of flour in the Lehmann recipe you referenced. When sugar is used in a Lehmann recipe, it is used at a rate of about 2-3% by weight of flour, and even then it is called for only when the dough is to be held beyond 48 hours (not 24 hours or less as in your case) or the pizza is going to be baked on a pizza screen. Above 5% and the sugar will negatively affect the yeast activity and prevent proper fermentation of the dough by permeating the yeast cells (through osmotic pressure) and overwhelming the yeast. When you added the entire amount of sugar to the water along with the active dry yeast (ADY), that also was not good for the yeast. It is common to add a pinch or so of sugar to the yeast/water mixture, but the yeast can't tolerate the amount of sugar you used, all at one time, without affecting its performance. I suspect the problem would have been less severe had you combined the sugar with the flour, where it would have been more uniformly dispersed within the dough and not in such direct contact with the yeast.
You also indicated that you used half of the dough from the Lehmann recipe to make a 10-inch pizza and that it was quite thin. The recipe you used produces a bit over 20 ounces of dough. If you used half of that amount for a 10-inch pizza, that is, about 10 ounces, the pizza skin would have had a thickness factor of 0.13, which is considered thick, not thin, and certainly not very thin as you indicated. I assume that you didn't weigh the dough ball to confirm its weight but rather just estimated it.
My advice to you is to forget the sugar (at least for a dough retarded for no more than 24 hours) and use one of the newer versions of the Lehmann dough recipe. I would also only use an amount of dough that you will need to make a pizza of whatever size you want. That way, everything will be in balance quantity wise, the thickness should be just right, and you should end up with a pizza that has the typical characteristics of a NY style. I have posted many versions of the Lehmann dough recipe at this forum, for several different sizes of pizzas, so there are many recipes available for you to choose from--from 9 inches all the way up to 18 inches. If you would like me to post one for a particular size pizza, let me know. If I don't have the size you want (I don't think I have one for a 10-inch), I will devise one for you (including substituting ADY for IDY, if you'd like).
As for having your pizza well done, you may want to consider lowering your bake temperature, for example, to 450-475 degrees F, and increase the bake time by a few minutes, or until you see that the crust has the degree of doneness that you prefer. Using this approach will have the effect of letting moisture in the dough bake off more completely and allow the crust to develop its color and texture more slowly than when using higher oven temperatures and shorter bake times.