I have always put my dough directly on the grill. No pan. There is a lot of opening and closing of the top because you got to keep it moving. Once the dough is sightly brown, move it to the top rack and close the lid. Check often because you can destroy a pizza in 1 minute. Sometimes I finish it for 1 min. on the bottom grill.
I'm finding out that there is no single procedure that works universally because each grill has it's own unique characteristics. I appreciate your suggestions because it give me ideas on how I could experiment with my procedure.
The one problem that seems most common is to get the top side to cook before the bottom burns.
My gas grill has a H style burner with lava rocks over the burner. I'm not sure what my BTU rating is but I'd say mine is lower than many others here who are able to get the top side to cook & brown the crust.
For my setup the preheated cast iron fry pan placed over the pizza helped a lot to cook the top side but I could still use more heat on top. Next I'm going to try a larger pan that extends past the tiles in hopes that more heat will flow up over the top side of the pie.