you might consider buying dough from a local pizza place. most will sell you a bag of dough for $5 and it cuts out a lot of the pain in the ass part.
try not cooking the dough first since your grill seems to run pretty hot (which is a good thing) - put the corn starch down on your pizza paddle, then the dough, then sauce it cheese it, etc, then slide it on the grill without cooking the dough first.
if your dough is wet, keep adding flour until it's just past being sticky. i used to do it without the stand mixer and would stir until i broke the wooden spoon and then kneed, adding little bits of flour throughout until i got the dough to a consistency where it's soft but not too soft where it doesn't hold it's shape when you poke it. when you poke it, it should come back out to shape it was before being poked. it shouldn't be sticky when you let it rise.