You will see lots of people with the WSK/E6/S6 cranking up their grills to 800+ degrees to try make Neapolitan style pizza....but personally I think this is a really bad idea. There are other styles and pizza dough that makes amazing pizza in the 500 degree range too.
That said, for a pre-made pizza, you pretty well want to follow the directions that came with it. The dough (and it's ingredients) and toppings etc were designed to cook at close to the temps recommended. Yes...take off the cardboard. You want the crust to cook right on the stone.
In general though, you always want to protect the bottom of the stone from direct heat as it will get scorching hot and burn your crust. I always dual-layer my pizza steel/stone with another diffuser underneath, and make some tinfoil balls to create an air gap. Preheat the grill and the stone to 450 - 500 for at least 30-45 min, drop on the pizza, and let it cook. Try not to open the lid and let the heat out while cooking...you can monitor the topping from the roof vent.
Raising up the stone very high in the grill works very well too...a popular method is to start your fire on the BOTTOM grate, and place the diffuser on the COOKING grate (yes, up high), then place your charcoal baskets on top of the diffuser for a big air gap and protection from direct fire heat, and finally, the stone on the VERY top.
You can really use anything to create the air gap....examples: