That's a tough one because the oven design and thermodynamics are not in your favor.
To give you a general idea, a commercial Baker's Pride deck oven, such as a Y-500, can handle about 150 16-inch pies an hour, at a temperature of around 475 degrees F, and with a good oven tender who can move 4 pies around at a time. The deck has a lot of thermal mass and a small cavity. Obviously, there is no way that you can get even close, proportionately, with a home oven and one pie at a time. If you have up and down ovens available to you, each with its own stone, at least you could improve your efficiency significantly. I assume for the moment that this is not an option available to you.
I have tried using two pizza stones, one above the other on separate oven racks, and have not detected a great improvement in the finished product, in terms of its quality or bake time. However, I think that increasing the thermal mass in your oven in other ways should help, along with making liberal use of your broiler element. For example, you might put two stones on top of each other, or one or more layers of tile along with the stone you are now using. Because of the greater amount of "stone mass" to preheat, it will take longer to get it to its maximum temperature--in direct proportion to the stone mass. However, once that temperature is reached, the stone mass will hold the heat longer also. Some oven heat will escape when you open the oven door, of course, but the stone mass will still be quite hot because of its relatively high thermal capacity. You can even open the oven door to get the bottom heating element to kick in again and close the door once it does. To make up for some of the heat loss in the stone mass as more pizzas are made, you might use your broiler element to keep the oven heat elevated, as by turning on the broiler element when you deposit a pizza on the stone mass. You might even use the broiler element to help bake the top of the pizza. Steve has used these techniques before for single pizzas, and he has even used tiles arranged vertically on the sides (he uses a double layer of tiles on the lower oven rack position to get greater thermal mass), so it appears that the approach works. How well it will work for 18 pizzas is an open question. If you decide to use layers of tile on a lower rack, I would leave some space at the perimeter so that the oven heat can reach the top of the pizzas.
I hope you will let us know how things turn out, one way or the other.