Thought I would update with last night's try at using one dough for both NY and DS.
Made the standard 700g of 70% hydration DS with a two-day cold ferment and at the 36-hr mark divided the dough, half went into the DS pan, the other half got a 20-second hand knead with the bare minimum of flour on the board, followed by a tight balling, then into an oiled Rubbermaid container. At the 44-hr mark the DS pan was removed from the fridge and sat at room temp for three hours. The NY dough came out of the fridge and the DS dough was stretched and then placed in a 120F oven for an hour to proof. With the oven on convection, got the bottom stone to 650F (!), opened the still cool NY ball and easily spun it out to 16", then formed a 14" pie on the peel, dressed with sauce, oregano, fresh basil, and a mix of whole milk mozz and sharp provolone, and cooked it in 4:15, convection on and no broiler time. Lowered the oven temp to 475 for the DS, cooked it without sauce, took about 13 minutes.
Both were spectacular - my son proclaimed the NY to be the second best he'd ever had and that he only wished I could make a bigger diameter pie. If you want a light, airy, and delicately crispy DS crust, I think this is the way to go for a dual-purpose dough.