Chris, I'm not sure if you're joking or not, but you can't use your pizza oven to fire clay
Different clays have different sintering temps, but 800C is about as low as you're going to want to go. That's 1472 F. Your oven isn't going to hit that, and, even if it could, it couldn't maintain it evenly over the course of a few hours.
Kilns are highly specialized equipment. They're insulated in such a way and have thermostats that regulate the heat so that they heat up very gradually and evenly over long periods of time (a day or more) and then cool down just as gradually. It's this very gradual heating and cooling process that prevents your pottery from cracking.
If you watch the video you just posted, almost every shot captures an incredibly traditional approach- from appearances, almost everything you see could be from 500 years ago. The sole exception, though, is the brief shot of the kiln. That's a very modern/technologically advanced kiln. I don't recall seeing any shot of Biscotto kilns- most likely because they're not as timeless looking as the rest of the process. I guarantee you that they're using modern equipment.
You've uncovered some important pieces of the puzzle, but, if someone's really going to reverse engineer these, they're going to need some serious ceramics background and equipment. No offense, but it's not you- nor, for that matter is it me. Over the years, I think we've had members with the necessary background, so, hopefully we'll get someone with that kind of knowledge again.