Benbuck, there's no need to apologize. From your initial post, it sounded like you have been making pizza for a while and wanted to up your game by aiming for something light and airy. We're all trying to help you attain that goal.
KABF is notorious for making dense bready crusts. I've eaten NYPD pizza, and, although it's not the best NY style pizza there is, it's lighter/airier than most chains that I've been to. Lightness/airiness comes from quick bake times (high heat/thick conductive stone), sufficient hydration and quality flour. I don't think I'm going out on a limb by suggesting that if you want NYPD's pizza, match their bake time and match their flour. That means commercial, high gluten flour. Most NY pizzerias use bromated flour, but since NYPD has franchises in California (where bromate labeling is stringent), I would guess that they don't use bromate. You might call your local pizzeria and ask- if it is bromated, then you definitely want to use bromated yourself, as bromate makes light and airy pies a LOT easier.
Your level of hydration, with proper flour, is pretty much where you want to be. 4% oil is way too much oil for NY style, neo or otherwise. NYPD feels a lot like a 2% oil dough.
Edit: I just called NYPD pizza on East Camelback Road in Phoenix (602-294-6969). They DO use bromated flour.