It's been quite a few years since I've had Joes, but, if memory serves me correctly, it didn't have the level of chewiness that one normally finds with fully developed All Trump doughs. You can get a tender crust if you underknead All Trumps, but, watching the video, I don't think they're working with an underkneaded dough. All Trumps (or other 14% bromated flour) tends to be the industry standard, though, so maybe they are using it and the tenderness is coming from the oven spring and thickness factor (or maybe additional oil). I would try two flours- bromated All Trumps and bromated 13% flour (King Midas Special, Spring King, Full Strength, etc).
The cheese is going to be Grande, and it's less than other pizzerias. On an 18" pie, that could translate into 10 oz. of cheese. They're renowned for being stingy with their cheese, though, so if you're making this at home, I'd use more.
From watching the stretching that they're doing in the video, I'm pretty certain that you're dealing with a mid hydration dough- at or close to the absorption value. For All Trumps, this would probably mean 62-64%
Sean, don't get too caught up with oven temps. A typical home oven at 550 is not the same as a deck oven at 550 because of the lack of thermal mass. Think about how quickly things cook while boiling at 212 versus baking at 212. Different materials, different heat transfer, different ball game. The only consistent way of looking at pizza baking is by time- a 4 minute pie in a pizzeria will match a 4 minute bake at home. I would say this is a 4-5 minute bake- and not a done at 3 minute bake and then pushed a minute longer for extra charring like you might find at a coal place. Joes might have a tiny bit of char, but it isn't much.
NY tradition has been same day or overnight ferments. Since Joes crust has never struck me as being one dimensional in flavor, I'm leaning towards overnight. With the number of pies they sell, I have a hard time picturing them having the room for that much walk-in space, so I think we're talking about a room temp overnight. Like the cheese, though, you have an opportunity to do better, so don't shy away from a superior 1 or 2 day cold ferment.
The thickness factor is most definitely .07 and not a fraction more. This is one of the thinnest crust pizzas I've ever eaten. It might even be as low as .065.
Oil is a bit of toss up. My gut feeling is yes, there's oil. I would give 2% a shot.
If you cold ferment for a day or longer, then I'd omit the sugar. If you do an overnight, then I'd add 1% sugar.
This is a pretty well kneaded dough. I wouldn't take it (or any dough) to window pane, but I'd go pretty close to smooth for an overnight and halfway between smooth and cottage cheese for cold ferments.
The sauce adheres pretty closely to my sauce philosophy- everything augments the tomato, nothing overpowers it. If you're going to add oregano, it should be just a pinch. Sugar, sure, just enough to offset the sourness of the tomatoes. Garlic, a little bit.
To be honest, I think one of the big reasons why you don't see any reverse engineering threads on Joe's is that there's no information out there to glean anything from. We can make a lot of educated guesses and come close, but without any videos of the dough being made, we're kind of flying blind.
Speaking of videos, the way the dough seems to handle, the thickness factor and the look of the finished pie all remind me a bit of Luigi's in San Diego. I would take a look at that thread.