"...fouls things up" Isn't that funny how hard it is to anticipate how little changes sometimes make a big difference inside the oven?
It sounds like we have similar environments in that the thermal mass of the stone is more than adequate to cook the underside of the pizza. In my upper burner / lower burner setup. I can just turn off the lower burner when I throw the pie - it makes no difference.
Since in your case, "top heat rules", I'll mention that the amount of radiatiant heat to the pie is proportional to the inverse square of the distance from the upper heat source. That's a fancy way of saying, It seems like you have a large air gap. If the distance between the pie and the upper heat is, say 4", and you cut that to 2", you should be able to cut the propane flow in half and get the same results. Of course, it's never that simple. In your case, if the lower burner is still going, by cutting the air gap you will also increase the convective heat flow as well, so you may get an even greater benefit.
Feel free to ignore my suggestion. I only share it because you have a rotisserie which tends to minimize effect hot spots (and I like to drive folks crazy).