That would be a such a marketing coup, I think it could be worth it. Name the place Really Clean Pizza.
The top element cycles on and off so the temp of the stone will vary noticeably depending on when you catch it. Depending on the oven, and on the distance of the stone from the element, and on the material of the stone, the final temp of the stone can easily be too high when the air temp reaches the clean cycle setpoint.
Some people shield the stone with a cookie sheet or aluminum foil and then remove before baking. Others start baking earlier into the cycle and don't stop baking as the continuous stream of pizzas will keep the stone temp down where it should be.
Mandatory is an IR thermometer so you can tell what the temp of the stone is and alter your timings and technique as necessary to manage it.