Welcome Frank. Great (and yummy-looking) photo!
For the blazing hot hearth you need for pizza, you need to reset your fire periodically. The oven will retain a LOT of heat and release it slowly over a period of many hours. But the hearth won’t keep a contact temperature of 800+ degrees F for more than about 20 minutes.
Why? Heat rises. And, every time you slap another pizza in the oven, the cool dough absorbs some of the heat from the hearth.
A commercial pizza oven, with a gas flame below the hearth, is constantly getting energy from underneath. The Barile is getting its heat from above.
Your best bet is to cook on one side, and after 10 pizzas sweep the embers to the other side. Add a log or two to refresh the flame, give it a little time to get blazing again, and make some more pies.
If the waiting seems too long, you should be getting a share of that pizza for yourself.
Hope this helps, and good luck!