I use King Arthur Pizza Flour, rolls thin and its ready to roll out in an hour or less. I also tried using parchment paper under the crust on top of the pizza stone on the grill and it worked great also; it may not work as well if you have a thick crust, but cooking a thin crust at 500 for 5 minutes the paper scorched a little but the crust was fine and easy to remove from the grill.

Live and learn. Hubs and I are into making pizza because there is nothing good available locally. I'm going to have to try this flour . . . So far I haven't found what I would consider a truly great recipe.

I have a good whole wheat recipe, if you want it, but I fire it at 475-500° F. I think I did try 515-525° F in the beginning. 475-480° seems to work best for getting the toppings and crust done just right. I don't know how it would do at higher heat.

Perhaps a commercial recipe designed for a higher heat oven would be best? I believe they're lower in moisture and meant to be done in under five minutes.

Pizza dough....flour, salt, yeast....and olive oil. Half teaspoon of salt per cup of flour, and 1 tsp of dry yeast....and 2 teaspoons oil. Enough water to mix and knead....between 1/4 and 1/3 cup of water....you can always add more or a little more flour or water...
Cover with oiled saran and allow to sit at room temp for 2 to 3 hours, punch down and refrigerate in an oiled zip lock bag for minimum of 3 hours....easily up to 5 days.
Flatten and shape while still cold. 2 cups of flour will make a big 15 inch pizza.
You will have better luck if you push it into shape rather than rolling.....and put lots...LOTS of corn meal on your peel!

I would think just adding less water would do the trick.

I have found that I get better results with 00 flour. I've been using Peter Reinhart's recipe for Neopolitan pizza dough.

00 flour won't make any difference if the dough is too wet, other than worsen the problem. The 00 flour is just ground a lot finer than other flour. What matters, regardless of the type of flour you're using, is the proportion of water, flour, and heat. If your dough is extremely wet, you can make it in a pan, but you'll have trouble using a peel. If your dough is not so wet, you'll be able to slide it off the peel having used only a slight dusting of flour. So the key is to get it as wet as possible but still have it be workable.

If you want to use 00 flour, that works, but the mechanics are a little different because it absorbs water a little differently. In any case, look for a flour that has a fairly high gluten content.

What makes your pizza dough spring is the sudden input of heat onto the dough surface. That heats the water in the dough, which creates steam, which blows up your dough. So you want your oven extremely hot and you want to put your dough on a material that transfers heat really fast.

I have not used that Unii but supposedly it gets up to over 900 degrees F, which is fantastic and on par with many professional ovens. You should be able to make phenomenal pizza with that. For a home oven, I use a half-inch piece of steel directly under the broiler. My last stove would get the surface of the steel up to almost 700 degrees, which actually turned out to be too hot. I think the Unii has a stone in it rather than steel, which doesn't transfer heat as efficiently and which is a better material for the temps that oven can produce. in fact, it should be pizza heaven!

We've made pizza at home a few times a week for many years and I've done it in a professional setting as well. There are lots of recipes for dough, but basically you want a slightly wet, but not too wet dough. You can start out with say, a cup of water and two cups of flour, and work up to around 2 3/4 cups of flour as needed, but you'll never want that much.

Some people say to weigh the ingredients and go for a 65% hydration or even more if you can, but weighing or measuring really isn't the point - you need to be able to tell by feel and not by measuring. That's how people cooked for centuries anyway.

A couple of other things - you should let your dough rest for a while once you mix in the water. It takes time for each granule of flour to become hydrated, and your dough will be a lot better if you give it some rest time. Anything from five or ten minutes to a few hours will help. Or do a sponge method, where you mix the yeast, water, and some flour a day early and let that bubble up, then add the rest of the flour, the next day.

Remember that 00 flour absorbs water faster and it also burns faster in your oven, so you'll need to play with your timings and ratios.

And if you use whole wheat for part of the flour, you can let the dough stay a little wetter than you might otherwise - the bran will take a longer time to absorb water and once it rises, it won't be so wet and sticky.

So this is a long way of saying what someone above said much more eloquently - try adding a little more flour or less water. But be careful - you don't want too much flour or your crust won't be as good. Just a sprinkling of flour, work that, and if you need more, add another sprinkling. And remember that your dough will feel wetter when you set it to rise than it will once it's risen, particularly if you let it rise in the fridge overnight or for a couple of days. If you work with cold dough, it's a lot easier to handle.

And finally it's your preference. Some people like a Neapolitan type crust, which is floppy and soft with a crisp cornicione, which is the thick part at the outer edge of the crust. Some people like what they call New York style, which is a thicker crust that you can hold up and which a lot of New Yorkers like to fold over lengthwise. That's a dumb move btw, and I can say that as a New Yorker, but you end up channeling the grease onto your shirt.

Anyhow, best of luck!

did use above recipe [lahey's] ... rose well, but added olive oil cuz I stored half ... put LOTS of garlic powder in the dough. I use AB's crust recipe for the most part though ... and for focaccia bread