Nate, I talk a lot about 4 minute bakes as a way of motivating people towards the fastest NY style bakes possible. In an ideal world where everyone had oven setups that could do 4 minute bakes, I would talk quite a bit more about 5 minute bakes. 4 and 5 are solid NY bake times, and for those looking for a tiny bit of crispiness, 5's a bit better.
While I'm pleased that you were able to produce one of your best pies to date, you're hitting the 'magic' bake times, and the top/bottom balance is improving, it's still too bottom heavy, imo, and, unfortunately, I don't see much you can do about it. Technically you're at 4 minutes, but 4 minutes without enough top heat isn't really 4 minutes.
As discussed previously, a thinner thickness factor might help- the less dough, the faster the cheese will melt and brown a bit. You could also extend the pre-heat, drive the heat up a bit further and toss the pie on a screen after a minute or two, or possibly lifting/doming the pie with a metal peel. Doming is more of a Neapolitan thing, but there are no rules against using it for NY as well.
It's so close, but it's not quite a cigar. If you're happy, and with pies like these you like these, you should be, then that may be all that matters, but, if you striving for something a faster, a bit more balanced, I think you're getting the most you can possible get from this setup and have to look elsewhere (to something like steel). Before you do that, though, I'd like to see how your current setup does without the false ceiling. 45 minute 550 convection pre-heat, stone 5-7" from the broiler, broiler on for 2-3 minutes of the bake. It'll probably be a 7 minute bake, at least, but, I just wanted to see what you can get without the ceiling.
