Lots of other things come into play (hydration ratio of dough, how quick u work dressing the pie as it's on the peal, how wet your sauce is etc). I cook between 63-67% hr and with a stone temp of 830 or so and mine come out decent. When cooking at those high temp 60-80 second pies, you really have to be monitoring the bottom and adjusting it around the stone after it's been on 30 seconds or so. Just practice some more and check out pizzamaking.com for all things pizza.
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Out of respect for the topic the OP posted, I won't get into my take on parchment paper, pizza screens, cornmeal, & semolina, as tempting as it actually is. :mrgreen:
You make an excellent point though, as it relates to dough hydration, stone temps, and especially, checking the bottom of the crust as it cooks.
In my Blackstone Oven, the top pretty much cooks at the same rate as the bottom, but I
always use the visual inspection of the bottom crust as the litmus test as to when to pull the pie out of the oven - this is best done with a metal pizza peel, which are ideal for pulling pizza out of hot ovens.
I check the temp of the stone as it is heating up with an infrared thermometer so I can dial in as close as possible the best temp for the dough I'm using. For non "00" flour, I look for a temp in the range of 650-700 degrees. 00 Flour can tolerate much higher temps, but those are not realistic for long periods in the Kettle PIzza insert kit, which is what the OP was asking about.
From what I've heard, the original Pizza Kettle kit (Which is what the OP has) is prone to the problems he's been having - bottom crust is done before the top is finished. This is discussed fairly extensively here, with a proposed solution:
http://slice.seriouseats.com/archiv...-and-kettlepizza-backyard-pizza-oven-kit.html