Welcome to the forum.
The Lehmann recipe you chose (and modified) calls for a very high hydration (amount of water relative to the amount of flour) to begin with--at the very top of the hydration range for that recipe (around 58-65%). Maybe you didn't realize it at the time, but when you used rest periods as advocated by varasano and others, you actually increased the hydration of the dough because of the improved absorption of the water by the flour. When you used the KA AP flour, you further aggravated the situation because the KA AP flour, as good as it is, cannot absorb the amount of water called for by the recipe. The reason for this is that the KA AP flour has less protein and less gluten than the KA Sir Lancelot flour called for in the recipe--11.7% protein versus 14.2%. (As a generalization, the higher the protein and gluten content of a flour, the more water the flour can absorb). If you used volume measurements rather than weight measurements, depending on how you measure things out you might also have raised the hydration level of the dough.
I suspect your dough would have turned out much better had you followed the Lehmann recipe as it was set forth. However, when you find yourself in a situation as you did, it is best to just forget the recipe and pay very close attention to the dough. What you want is a dough that is smooth, silky, elastic, and a bit tacky--not wet or dry. If it's really wet, as it was in your case, just add more flour--a teaspoon or tablespoon at a time--and work it into the dough. If the dough is dry, add water--also a bit at a time--and work it into the dough. I carefully weigh the amounts of flour and water I need, and even I have to make minor adjustments to flour and water to get the dough just right.
Since I posted the recipe you used, I have modified it to lower its hydration by a few percentage points. If you go to the thread I recently posted at http://www.pizzamaking.com/forum/index.php/topic,1453.0.html
you will find several possible Lehmann NY style recipes to choose from. If you want to use autolyse or other rest periods and other procedures, you should feel free to do so but keep in mind that making those kinds of changes will alter the dough somewhat and change its finished characteristics. I suspect that you will likely have to make other adjustments, such as to flour and water, and to take other measures, to achieve the end results you are looking for.
I'm sure that in due course you will master the techniques of making good high-hydration pizza doughs, whether it is a Lehmann NY style dough or any other. The principles involved are pretty much the same.