I think you mean 'conveyor' oven rather than 'convection,' correct?
I googled 'The Crowbar & Grill' and noticed that you are planning on selling 'high end' food and beer. IMO, neither American, Tavern or Chicago Thin Crust are 'high end' styles. Neapolitan, as perceived this moment by the American public, is probably the 'highest' end style, but you won't ever get a Neapolitan pizza out of a conveyor oven. You next best bet, imo, is Neo-NY or NY. Your conveyor might be able to handle as low as 4 minute NY bakes, giving you something high-ish end, but still being highly accessible, highly marketable to your late night college crowd, as well as offering slices that warm up nicely.
I believe one of the factors in getting fast bakes out of conveyors is maximizing bottom heat intensity by utilizing dark baking discs, although if the oven is pumping out enough BTUs, you might be able to get away with screens. How many BTUs is your oven?