Does the stone sit flush in the rotating panel? If it does, you can favor the top heat a bit more by raising it, just make sure you don't raise it too much or you'll lose the impact of the shielding, as Jro saw. 4 or 5 of stainless steel washers should do the trick.
This will allow you get a bit more relative heat to the dome while keeping the stone in a lower position, so that the side flames are maximized- which I believe could be an important part of the equation.
Also, I know that doming has been discouraged a bit in this thread, but I wouldn't give up on it yet. If 800 ends up being the sweet spot for a 90 second bake without doming then perhaps 850 or 900 can make for a happy 60 second bake with doming towards the end- assuming, of course, the oven can reach those temps. I think, eventually, as you continue to find ways to decrease the bake time, the 60K btu burner might start showing it's limitations. Maybe.
One thing to bear in mind regarding the gap between the stone and panel and doming... This will extend the pre-heat a bit, and, with a hotter dome, if high temps are causing components to fail, then this will exacerbate that. There's also aluminum above the top stone. If that hits 1100ish, you've got a problem. It also might impact recovery time between pies a bit (you might want to try thicker/thinner washers). I do think, though, that a very small gap and doming might make a difference in the balanced 60 second bake quest.
One last piece of advice. The powder coating on the outer shell looks a bit iffy considering the potential temps it will be hitting. I wouldn't store this outdoors.