I can't speak to the pan question, but if you want to improve your NY pies, you need to work on your grill setup and get more top heat by adding some kind of false ceiling closer to the pizza to radiate the heat downward. All grills have top bottom heat issues and it's very difficult to get the top brown without burning the undercrust.
You can also go with a less conductive hearth, such as fibrament or quarry tiles combined with some kind of deflector so they don't get damaged by the heat.
If you're looking for a less NYish more American/Chicago thin crust-ish crispiness, you can pre-heat the stone to a lower temp and leave the pizza in for longer with the pellet burner on high, making sure not to lift the lid too much or you'll lose the collected heat.