How can I produce a more soggy Neapolitan pizza crust?
It sounds like you're doing several things differently than the recipe (different flour, different temperature, different baking surface...) though I don't actually see shaping/baking instructions on the recipe you linked. If you want to stick closer to that recipe (than the other answers...), here's a few other thoughts of potential problems and a few things to try to alleviate these potential problems.


Baking too quickly or overcooking. the baking steel will transfer heat more quickly than a baking stone, a perforated pizza pan, or a sheet pan. Try one of those other baking surface options if you have them, or preheating your steel for a shorter period of time, or cooking for a shorter period of time.
Different flour. doppio zero flour is (likely) much more finely ground and more highly refined than your bread flour; these differences will impact how your bread behaves, such as water absorption and retention (in addition to the temperature comment you made). You might want to try increasing the water, to see if that does something you like (this recipe is about 65% hydration, so you've got some room before the dough gets really sloppy). Bread flour and 00 flour  will (likely) have similar protein content, but you could check that from the respective producers, also.  Despite your cost and temperature concerns, have you tried 00 in this recipe just once to see if there's a difference?
Shaping.  Looks like you have a system, but perhaps you've got the dough just a bit too thin in the middle?  Might be worth making the center slightly thicker as a test.  Also might want to try making one a bit bigger.
If you're cooking one at a time, try cooking two at a time.  They'll each be absorbing some heat, so baking will happen slightly more slowly.


Other questions:


are you indeed letting the dough ferment and rest for this long? 8-12 hours of initial ferment seems uncommon for conventional yeast. I've seen this long initial mix-and-rest for a (no-yeast) autolyse step, or for (very) sour sourdough.  I wonder what the intended effect is...
I'm also surprised there's nearly zero kneading; gluten development will be... different. It seems like the dough will be lumpy, and the gluten development wouldn't be as uniform. Or, perhaps after 2.5 days fermentation this is enough time to have the dough work itself out on its own.  The "bread in 5 minutes per day" franchise also suggests multi-day fridge storage, so I think this is probably a good thing in this case.


Looks good; I think I'll have to try this.  Good luck!  Post back if you discover some improvements...