Of the three flours you mentioned, the only one that would work properly with the set of baker's percents you mentioned, including a hydration of 63%, is the KASL. And, if you used ADY for that dough batch, you should have rehydrated the ADY in a small amount of the formula water at a temperature of around 105 degrees F for about 10 minutes. At that point, the rehydrated ADY could either be added to the rest of the ingredients in the mixer bowl or to the rest of the formula water, which would ideally be on the cool or cold side for a dough that is to be cold fermented.
The KA Italian flour is a domestic "clone" of the Italian 00 flour. It has a protein content of about 8.5%. By contrast, the KASL has a protein content of 14.2%. Apart from the fact that the KA Italian flour is not intended to be used to make a NY style pizza, it won't work with a hydration of 63%. You would perhaps need a hydration of around 54-55%, and maybe even a bit less than that.
The other (unnamed) Italian flour (00 flour) you mentioned would be prone to the same hydration problem as the KA Italian flour, and using rehydrated ADY for the dough made using this flour would not save it. A 63% hydration would just be too much for this flour. Even the Caputo 00 Pizzeria flour, with a protein content of 11.5-12.5%, which is higher than most 00 flours and can tolerate higher hydration values than other 00 flours, has a rated absorption value (hydration) of 54-56%, although it is possible to use a somewhat higher hydration if you have a very high temperature oven to bake the pizzas. Like the KA Italian flour, the 00 flour is not intended to be used to make a NY style pizza. Both of these flours are intended to be used to make Neapolitan style pizzas, although I would proceed with caution when using the KA 00 clone flour for that style.
There are apparently some stand mixers, like the Bosch mixer, where you can just about throw all of the ingredients into the mixer bowl and start mixing/kneading the dough. That is uncommon. Most other home stand mixers require a more organized sequencing of the ingredients to get good results.
I am pretty certain that the dough that you saw in the Lehmann video used IDY. IDY can be added directly to the flour, as can the salt. Some people put the IDY on one side of the flour and the salt on the other before starting the mixing operation, or alternatively they dissolve the salt in the water before adding the rest of the dry ingredients. Even Tom Lehmann will tell you to rehydrate ADY if you use it, in the same manner as I described above. There should be no problem rehydrating ADY that comes right out of the refrigerator. Using warm water at the proper temperature should be adequate.