I've done it in the oven and on the grill several times. But, it is sooo good, we've been having it once a week and since you bake at 450°, that can heat up the kitchen pretty fast in the summertime. I'm not familiar with Detroit pizza, but the comments on the site suggest that's what it is. It's very doughy but really crisp on the bottom and edges.
I have a gas grill with three burners. I start with all of them on and get the temperature to 450° and set the pan over the middle burner. Close the lid and bake for 7 minutes. Then, I turn the middle burner off and bake, with indirect heat for 8 minutes, adjusting the other burners to maintain 450°. When the cheese on top is turning brown, it's done. These are the times that work for me, but I presume all grills are different.
One thing you must be very careful of is making sure you take a silicon spatula and loosen the pizza from the sides of the pan immediately after you take if off the grill (or out of the oven) or the cheesy caramelized edges stick and you'll really mess up your beautiful pizza. (And you don't want to scratch your pan with a sharp knife.) The first time I made it, I tried to use a plastic knife and it melted.
Once the edges are loosened, because you've put the dough in the pan with lots of olive oil, it slides right out of the pan - but it's very heavy.
It is really fun to make and just delicious. I use Chris Bianco's no cook tomato sauce - ridiculously easy and delicious.
Edited to add link for tomato sauce.
https://parade.com/608975/alison-ash...-tomato-sauce/