Scott, just to clarify you are referring to what appears to be my max temp right?
Jon, with the quarry tiles blocking the thermostat and your oven generally running a lot hotter than normal, I'm relatively certain, should you wish to take the risk, you could hit Neapolitan temps for the hearth. With cordierite, that's probably around 750. But the ceiling, though... Neapolitan oven ceilings get very very hot and there's also a lot of heat coming off the burning wood to the side. With the heat source on the bottom of the oven and the cordierite hearth in the way, I'd be surprised if your quarry tile ceiling hits the same temp as the hearth below.
I don't know, maybe you could crank the hearth to 750, bake the pie for about a minute and then, with a metal peel, lift it up a fraction of an inch and 'dome it' against the ceiling. I think that's a bit of a long shot, though.
That said, ignoring the ceiling (quarry tiles) and the gap between them and the cordierrite, how close do you think I can get the stone to the bottom of the oven and be ok?
I think that the closer you bring the hearth to the heat source the quicker it's going to pre-heat, which, in turn, might give you a larger discrepancy between the ceiling and the hearth. You could, in theory, pre-heat the oven until the hearth is a bit above the target temp and then turn the oven off, allowing the heat to travel upward to the ceiling.
What I am dealing with is an obviously inaccurate dial (550F = 650F and beyond), the thermal probe is located in the isolated upper region of the oven, and last but not least the nice thermal mass of the stone and tiles makes it difficult to accurately adjust the temp down to the desired range.
Your oven was a bit wacky to begin with. Now that you've block out the thermostat with the quarry tile ceiling, the thermostat is completely useless. I think it's pretty safe to assume that when you turn your oven on, the bottom burner will stay on for a very long time. You should be able, with some trial and error, to let the clock do the work for you. Turn the oven on, wait 20 minutes and then take temps of the bottom of the hearth, top of the hearth, quarry tiles, as well as the oven ceiling. Try 30 minutes. 40 minutes. 50 minutes. You may need to turn the oven on for a while and then off for a bit, so the ceiling can draw some heat from the hearth. There will be a magical number of minutes of either oven on, off or both that gives you that perfect pizza baking temp.
Bear in mind that opening the door to take temperatures will allow heat to escape, so, if, say, you hit the target temp at 50 minutes after opening the door at 20, 30, and 40, you should probably try 40 minutes with the door shut the entire time.