Tran, that was overfermented dough. Not hugely overfermented, but still past it's prime.
There's prevailing theories here, and elsewhere, that as dough overferments, the yeast consume more and more sugar, resulting in a dough with very low residual sugar. I feel differently. I've talked to experts about this, and, the theory I resonate the most with is that yeast, in a bread environment, don't eat that much sugar (as opposed to a beer environment where they feast). The lack of yeast activity as a dough overferments isn't the result of lack of nutrients, but a result of an alcohol rich (and possibly acid rich) inhospitable environment.
The bottom line is that overfermented doughs burn a lot faster than those with less fermentation. I'm 99% certain that it's sugar that's to blame.
As far as getting the egg to work right, unless you hang a stone ceiling, I don't think there's much hope for getting close to a decent hearth/ceiling heat ratio. Even then, I think it's hard to do.
Next time, close the top vent (if it isn't already closed) and make sure the gap around the firebricks is equal on all sides. How much gap is there between the s/s pan and the walls? It needs to be a little bit wider than the gap you have for the firebrick. Assuming the gap is wide enough, go with the s/s pan under the hearth (with more ceramic briquettes) and time the pie so that it goes in with a hearth temp of 500 (or omit the pan entirely and go with a 500 deg. hearth temp bake). It may seem low, but with intense heat coming up from the bottom burner (even with the pan in the way), the hearth will jump in temp as the pizza bakes. This will give you a good idea how much heat you can collect in the headspace to bake the top of the pie. I don't think that burner, in that scenario, will pump out enough heat to give you something truly Neapolitan-ish, but it should give you enough umph for a 3-5 minute pie.
You're basically baking your pizza during the time it takes for the blazing heat on the bottom of the stone to travel to the top.
You can launch the pizza through the slot, right? In this scenario, you want to keep the lid on. That collected heat is the difference between a pale top and a done top.
The one downside to this is that, by the time the pizza is cooked, the stone will be considerably hotter, so if you want to do another pie, you'll have to turn off the burner and wait for the stone to cool- most likely for at least 15-20 minutes. With a second pie, since the stone should be more equally heated, you might want to bump up the starting temp to 550, but not much higher.
You might be able to recreate this effect a little easier by using two layers of firebrick. This will cause the heat to travel a little slower AND it will move the pie closer to the ceiling- both good things. By the way, with the lid on, you've got at least 3/8" clearance on all sides of the existing firebrick, right? It looks like the the firebrick has enough clearance on the grill, but the lid slopes inward, so it's possible that there may not be enough clearance on the sides of the lid. 1/2" clearance is ideal, but, since you're dealing with a small space, I think you can trim it to 3/8", but I wouldn't go less. Should you add another layer of brick, you'll definitely want to size it accordingly for the sloping lid. If an extra layer of brick pushes you too close to the ceiling, then I might try a cheap round pizza stone on top of the brick. That kind of stone is notorious for lack of resistance to thermal shock, but, with the firebrick between you and the burner, I think you might be alright. Just make sure you've got the gap. Air flow from the burner to the top of the lid is critical.