Vince, bake directly on the stone, yes. Use a wooden peel to launch and a metal peel to turn and retrieve.
I judge gas ovens by the BTUs per square inch of deck real estate. Whatever oven you're looking at- take depth and width and multiply them together to get the square inches and then divide the total BTUs per deck by that number to get BTUs/sq. inch.
The best ovens you get can get, the Marsal MB and the Baker's Pride Y600 are 55 BTU/sq. inch. You can find ovens that will go all the way down to 30 BTU/sq. inch, but 40 is about as low as you want to go. Touch base with Norma. Her oven is 30 BTU/sq. inch. I know that when she cranks up the heat, the bottom of the pizza burns before the top is done, but I don't know how low of a bake time she can hit while still maintaining an even top/bottom heat. She might be able to hit 6 minutes, but I'm not sure.
Even if Norma can comfortably hit 6 minutes, I'd still shoot for a 40+ BTU/sq. inch oven, as this will give a bit more flexibility down the road. For instance, if, at 6 minutes, you're encountering too much bottom heat, you can slow down the bottom with a less conductive hearth such as Fibrament. In order to accommodate for this handicap, though, you'll need the extra 10 BTUs/sq. inch.
Btw, 6 minutes, for NY style, can be incredibly generic. Norma's pies aren't generic, but she's the exception to the rule. If you want some 'wow' factor, you might want to follow your initial inclination towards a faster baked Neo-NY pie. This makes your oven quest a lot more difficult, but, at the end of the day, your product will stand out that much more.
