Before I got a wood-burning pizza oven, I used @tony b's technique in the KK: 550°F dome, heat-soak for an hour, pizza stone on the top grate (later I used the pizza stone topped with a baking steel, which enabled a bit more leoparding on the bottom without burning the top), and let the KK recover about 8-10 minutes between pizza launches. I made mostly NY-style or Chicago deep dish. One can't (or at least I couldn't) make a true Neapolitan on a KK. Or maybe because I was unwilling to risk running my KK at 900°F. 00 flour doesn't work as well below 750°F.
As Tony said, you have to match the dough / flour to the temperature you plan to use. As I remember, large lump charcoal made it easier to achieve and maintain the temp. I have a KK23 so the KK32 may be a little different.