Norma, the modifications I'm recommending aren't going to be easy, especially since both involve adding weight to the oven, and, if your floors are having trouble with the weight, then this will exacerbate that issue, but, if, as you consume your BS NY pies, you continue to recognize their superiority and your motivation to match these with your market oven grows, I sincerely think that if there's a will, there's a way.
Basically, as you've witnessed, if you crank the heat on the deck ovens, the bottom burns. You can correct this heat imbalance using two methods. The first is adding a brick ceiling. Since your existing ceiling won't be able to bear weight, you'll have to build some sort of frame for the bricks that sits on the floor. You should be able to test this with only a portion of the oven- maybe an 18 x 18 area. The brick ceiling is a classic approach at bolstering top heat, but the bricks aren't light. Kenji, over at Slice, has made considerable headway proving the effectiveness of low thermal mass ceilings. While I think the bricks are a sure fire way, you might be able to improve the heat balance with something as simple and easy as either a heavy duty foil ceiling or lightweight steel sheet ceiling that's a couple inches lower than what you have now. Both are worth playing around with.
The second method is a bit easier, but may not be quite as effective. I'm not sure what you have under your stones right now, but I think the flame of the burner hits the exposed stones. Whatever you have under the stone, my recommendation would be to add a steel sheet with an air gap between the sheet and stones. This air gap mimics the air gap you get with the washers in the blackstone.
Nothing I'm recommending would irreversibly alter your oven in any way. I know you have other repairs/considerations you're dealing with, so I completely understand if you wanted to wait, but I did want to toss these ideas out there so you could mull them over.
Maybe I'm reading too much into it, but your "I think I like NY style pizzas best now" comment seems like it's saying "Neapolitan used to be favorite pizza, but, now that I'm doing fast NY style bakes on the BS, those are my favorite." It feels like Steve's modded grill pies planted the seed in your mind of what fast baked NY style can be, and the BS is proving it beyond any shadow of a doubt. If this is indeed, where you're preference is currently at, then you and I are in exactly the same place.