It sounds like they might have one oven set to 700 and another at a lower temp. Did both pizzas get the two oven treatment? 8 minutes at 700 would incinerate pizza.
How floppy were the slices? Any char on the undercrust?
How does the thickness factor compare to the photo on the website? I'm hoping it's a bit thinner, because, for NY style, a rim of that size is pushing it.
Reverse engineering can be exciting, but, in this instance, I think you might be able to quickly surpass this pizza on your own with a solid recipe and the right oven setup.
If you really are dead set on reverse engineering this, then, the next time you go, bring a camera. Get an upskirt. Take a shot of the guy making pizza, and, if possible, the kitchen. Look, obviously, for tomato cans and bags of flour. Use the bathroom- sometimes they'll stack flour in a hallway. Look for a walk-in. See if they'll sell you a dough ball, and if they do, ask when it was made, and, while you're talking about the age of that dough, ask how long they refrigerate the dough in the store ("I'm trying to match your results exactly").
Watch the guy stretching the skin carefully and see how much force he has to use. See how much bench flour he's using. This will go a long way in telling you hydration and kneading time.
If you do dumpster dive, be careful. Don't get caught.