We never use a stone on the grill as I heard the direct hear is bad for them and could crack it.
Anyway, we do the flip it method as follows.
Crank the grill up pretty darn high and let it warm up.
Get your dough ready and leave it a bit thicker than normal if you generally make really thin pizza. Needs to be able to handle it well.
Put some oil either on the grill grates or on the dough to prevent sticking and pop it on.
Turn the grill down to low and let it cook for maybe 2 minutes.
Take it off the grill and put it cooked side up.
Turn the grill back up to high so it can warm back up.
Dress with sauce and toppings.
Oil the grill again if needed and then put the pizza back on the grill.
Turn the heat down to med-low and let it cook for 3 minutes or so.
If the dough starts to get charred, you can turn the burners off and leave the lid closed to cook/melt the cheese and toppings.
It's finally warming up here in WI so I bet we'll be doing this soon enough.