A friend who has made his own dough and made pizzas anytime he was staying at a place that has an outdoor brick pizza oven finally bought an UUNI about 2 years ago. Gas, but I think the ones that allow for a lump or two of wood to be slipped in for the smokey char on the crust.
So he would recommend that.
I got a pizza disk for my Kamado Joe II and it was not the easiest thing to keep the pizza disk scorching hot by the time you wanted to make a second and then third pizza. (I did NOT have a lump coal cage at that time, but have recently bought one on Black Friday Discount.)
IT'S ALL ABOUT THE DOUGH
I made my own dough the first time and it was far and away the best. I did the 24 hour method that ended up sliding into a 48 hour thing.
Second time I used Trader Joe's dough and it was nothing compared to the homemade stuff, plus it was more difficult to work with.
Third time was the frozen ball of pizza dough from Central Market. Basically the same as the Trader Joe's experience.
The elasticity of the homemade dough was the difference. The other two doughs would stick and/or tear. The Homemade stuff was so much better to work with, but you have to plan ahead 24 to 48 hours.