Paul, a few observations
First of all, it looks like you're getting sauce on the rim and it's effecting crust browning. When you form the skin, you want to sauce to about 3/4" away from the edge and you want to sprinkle cheese another 1/2" in from that. If the sauce is migrating during the bake, you'll want to use a thicker sauce and/or possibly less sauce.
A big part of what defines NY style is the general lack of toppings. If you like a lot of toppings, then I think you'd be better off going with American style, which is much more topping friendly. If you like pepperoni and want it in every bite, I recommend going with a much thinner slice- that way you can cover the whole pie but not go overboard with the overall topping weight.
It's hard to tell, but I think you might be using a bit too much cheese as well. Are you measuring the cheese? If you are, how much are using and what's the diameter?
I think I recall seeing you mention frozen dough balls in another thread. Have these been frozen dough balls? If they are, I highly suggest making the dough yourself. The fluctuating temperatures you're baking at have impacted consistency, but I think the frozen dough has messed with your consistency as well. Frozen dough can fluctuate massively in levels of fermentation/residual sugar. If there's low residual sugar, you might see insufficient browning as compared to previous bakes, and if there's a spike in sugar, you might see abnormally quick burning. If you're making the dough yourself and controlling the variables, you can produce a product that browns the same way every time.
Pre-heat Consistency/Cool Downs
It seems like your temps (and results) have been a bit inconsistent. I think, rather than focusing too much on the IR thermometer readings, you might want to zero in on time. Rather than trying to hit a target temp, I'd use time for measuring your pre-heat instead. For instance, I think a 40 minute cleaning cycle and a 20 minute cool down might give you good results. Also, it's absolutely critical that you cool the stone down with the door closed, not open, or the front of the stone will be substantially cooler than the rear and you'll get uneven bakes.
Clean cycle 40 minutes, 20 minute cool down (door closed), then take the temp of the stone. If it's a lot higher than 625, then close the door and give it 10 more minutes (and going with a shorter cleaning cycle on the next occasion). There's going to be a clean cycle/cool down time that will give you a perfect first pizza, it's just a matter of dialing it in, making small changes and opening the door as few times as possible. Now... for the second pizza, that might get a bit tricky, but you shouldn't have to re-feed it with that much heat- maybe 5 minutes of cleaning cycle and 5 minutes of cool down.
The top shelf + broiler was definitely too intense. That's actually kind of encouraging, since most gas broilers are typically a bit weak. You definitely still want to use the broiler, but you should put the stone on the second shelf down and use the broiler for part of the bake- maybe going with an approach similar to mine- 3 minutes without the the broiler and 1 minute with. The nice thing about the closed door cool down is that the top of the oven will be evenly heated as well, giving you much more even top baking.
For NY style, I would shoot for 4 minutes, top and bottom. That could be, with the right amount of toppings, a 625 stone temp, or it might even be as low as 600. This stone isn't all that thick, but perhaps it's a bit more conductive than your typical cordierite.