The way I'm doing it with a skillet and the broiler is probably as close as you're going to get to a real pizza oven. I've never been able to get a pizza stone hot enough so that the crust cooks super fast. I have an infrared thermometer that goes to 716°F and the skillet got hotter than that and the thermometer just read Hi. Onto the skillet and then immediately under the broiler on high just a few inches away. It literally only takes at most 3 minutes and the pizza is done.
I did try using a pizza stone on my grill a few years ago and it cracked. I've been using the skillet ever since and it's actually only 10.5" I'll probably get one of these 15" cast iron pizza irons.
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