While I am not sure that this would not work well, I have elected not to try it for the following reasons:
1. Stones cool slightly when you slide a room temperature pie on them. While the bottom stone would continue to receive heat quickly by the bottom oven coil (radiant + convective heat), the top stone would only see the hot air (convective heat) and not reheat as quickly. Conversely, the top stone would be subject to much more heat from the broiler element and may brown well before the crust is cooked.
2. Like you, I cook at 550°F and it takes about 8 minutes to fully cook a pie. It takes me nearly 8 minutes to grab the dough ball and turn it into a pie ready to slide into the oven. Working two at once, I would need to create each pie in 4 minutes or have a helper.
I rarely crank out more than four at any one time, but have had success in starting a bit early and allowing the first one to sit on a screen (to stay crisp) on top of the oven, while the second one is cooking. This will allow me to serve two several minutes apart. Once the crowd has two pies to chew on, the demand slows down a bit and my normal 8 minute cycle is fine, especially if there is other food available.
I’m not sure what is driving your desire to crank out 6 pies in rapid succession, but for me it’s having a crowd over for pizza. When I do, I like to think of have them into my home as an event, not just a dinner, so having serving over 30-40 minutes (2 at first and 4 more in 30+ minutes) has not been a detractor. Often, once the first few pies are out, folks are migrating over to my prep area and I’m walking them though the process, as I form the dough and put it all together, so it may slow down even more.
Sorry I was not able to provide direct experience to address your question, but I’m hopeful that I was able to help with a solution.