it seems incredibly difficult to make a pizza that tastes like real new york pizza at home. has anyone had success?
It depends on how you define 'success'
This is probably going to get me in trouble, but there's lots of people who eat quasi-NY pizza outside of the NY metro area, enjoy it, and then, in turn, duplicate that at home. It's not really high heat, short baking time puffy chewy non bready NY pizza, though. There is a small group of people, though, that either live here or have lived here (or have visited extensively), that know and understand pizza bliss and have successfully recreated that bliss in a home oven. It's not a large number, though. And none of them have your dietary restrictions
I'm sorry to say it, but you've kind of handicapped yourself on two fronts. Equipment and ingredients. I've become a lot more vocal about fibrament's inadequacies due to the growing number of people with experiences such as yours. It just doesn't quite have enough conductivity for quick bake times. Other the the stone, your dietary restrictions are the second half of a one two punch. I sincerely believe that if you had either a better stone or a willingness to work with purported less healthy flour, your chances would improve tremendously. If you could work with both a better stone (1" cordierite or soapstone) AND All Trumps bleached bromated (enriched) flour, with your current level of knowledge/dough handling skills, the pizza of your youth would be a piece of cake. You could do it in your sleep. Which makes your current predicament a little frustrating.
Frustrating, but not necessarily insurmountable.
Caputo flour is unmalted, and that works fine for 850 deg wood fired ovens. Unmalted flour, such as the Bob's Red Mill Organic flour you're using, does not work well in lower heat situations, though. Without the enzymes in the malt, less sugars are generated, which, in turn, stunts yeast growth and coloring. For NY pizza, you need both.
I know artificially derived vitamins are off your list, but what's your feelings on malted barley flour? Ideally, you could find a malted unenriched bread flour, but I don't think such a thing exists. It's either all the additives or nothing. Bob's Red Mill sells malted barley flour, so you could add it yourself- if you were willing to use it. Malted barley flour would improve your crusts dramatically.
Sugar, although not normally absolutely necessary, becomes a necessity when you've got an impaired stone. What's your feelings on agave nectar? That should give you browning, and, unlike honey or fruit juice, has a fairly neutral taste. Agave is rich in inulin which is a probiotic and relatively healthy. Also, what about fructose? Does your diet allow that? Fructose has been rumored to be attached to a few health issues, so I wouldn't use it to make desserts on a daily basis, but a little bit once in a while in pizza may not be the end of the world. And, for what it's worth, it's low glycemic. Fructose browns faster than any other type of sugar so you wouldn't need much.
I recommended 70% hydration because I want you to have experience working with a dough that was too hydrated. I guess if 64% is troublesome, maybe 70% might be a little too much, but I want you to keep increasing the water until it's absolutely impossible to work with and then dial it back a tiny bit. Next time, try 67%
That's the ingredient front. I think you're at a point now where the time might be right for pushing your fibrament with a little careful broiling. You've been doing the 90 minute preheat, right? I don't think it's making much of a difference, so dial it back to 60. Put the stone on the top rack of your oven (making sure you have enough room to work with). After the 60 minute preheat at maximum temp, crack open the door and put the broiler on for... 5 minutes. Try another pie with 10. Bear in mind, there may be a small chance this may crack your stone, but I think if the stone is fully preheated, the extra thermal impact of the broiler shouldn't be too much for it- as long as you don't overdo it.
From the photos, it looks a little like you're using the floured peel that you used to deliver the dressed skin to the oven to remove the fully cooked pie. That's a bit of a no no because it gets uncooked flour on the bottom of the cooked pie. This uncooked flour tastes horrible. Use a metal peel or metal cookie sheet for removing the pie.
Re; 3 day vs. 2 day dough. Malted flour has enzymes that produce sugar in dough that is both food for yeast and promotes coloring. Unmalted flour still has these enzymes, just much less. So as you leave dough in the fridge, the more sugars are created, the more crust color you get. To a point. Eventually the yeast activity will increase and residual sugars will decrease.
In another thread it mentioned getting the pizza out of the oven straight to a metal tray so the crust steams a bit. You've implemented this, correct?
I know, from the other post, your ingredient ratios, but how about posting your process? A pre refrigeration and post refrigeration photo of the dough would be hugely helpful as well. Unmalted flours make relatively yeast unfriendly doughs and I want to make sure your critters are doing their thing.