Using screens is probably the easiest way, but you always end up with a pizza that was baked on a screen.
I know exactly what you're talking about because I've done that for parties more than a few times, usually with one pizza baking in the oven while another one bakes in the grill. When I've done that, I probably used screens for at least half of the pizzas because one person alone simply cannot tend two ovens 50 feet apart and stretch/assemble pizzas and still crank out the pizzas fast enough to keep up with demand. Just by stretching a few skins ahead of time and putting them on screens, then not having to worry about peeling those pizzas onto a stone the same size as the pizza, the work becomes considerably easier and more efficient.