PB, do you have a larger photo of the oven setup? I can't really see what's going on. The fan is visible on the back wall of the oven, right?
Thick stones, with their extra thermal mass, will perform better than thinner stones, but the downside is that they take considerably longer to heat up. If you're not open to the idea of 90+ minute pre-heat (and the energy bill they might entail), then I think you're ready for steel. 540F with 1/2" steel is perfect for NY style pizza and will give you all the undercrust char you could ever want. The only downside to steel is that it's heavy/hard to get in and out of the oven.