Hard to get good results making pizza on a bbq, not enough top heat, results are usually a nice bottom and under cooked top or an over cooked bottom and a nicely cooked top. There's some simple things you can try to improve baking on the bbq, putting your pizza on a screen for part or possibly the entire bake, a deflector of some sort on the top rack (tinfoil is the easiest thing to try) to get more top heat. My personal experience for better results on the bbq is pizza on a screen directly on the rack, no stone/steel, slows down the browning on the underside.
Home oven 500-550F is a much better way to go, A/P or bread flour will work perfectly fine. If you aren't comfortable with launching directly onto a steel use a screen, after 4min the pizza will slide right off. I'm baking at 535F 7-8min and I get a nice slightly crispy crust, 30sec-1min longer even crispier.
This should work nice for a home oven (fermentation based approx. 22.5C) it's a same day room temp recipe, 8hr total fermentation.
Flour 100%
water 63%
salt 2%
sugar 1.5% (cut back if browning too quickly, may need none at all)
oil 1%
ady 0.1% (0.078% idy)
I use ady, not for any particular reason. I hydrate the yeast in 25% of the water at 85-90F and the remaining is cold out of the fridge. Mix/knead, ferment for 1-1.5hours, divide into balls or reball if batch is only for one pizza and ferment for remainder of time, 8hrs total time.
This site should help you if you need to change the fermentation temp, time or would like to do a combination of temp's, pretty straight forward to use. Input time(s), temperature(s), choose yeast in pull down top right, click calculate yeast percentage... button, done!
http://www.shadergraphics.com/Good luck, any questions ask away.