Shaun. Before doing the variation on Mike's disk mod, my preheat time was about 20m. After plugging up the sides and moving the sand bowl forward, my heat up times dropped about 50% to around 10m.
Today, I took the disk out of the lid and added that vortex generator (aluminum foil lip) and I noticed it was right at 6min to reach a hearth temp of 700.
Here is what I think is going on. I think that aluminum lip directed the hot air down towards the hearth instead. So (some of) the air flow is coming up from the back and hitting that lip and going down towards the hearth beforer coming out the front.
You can likely reproduce this effect by turning your lid about 30deg left or right. This will cause the heat to have to turn before going out the front lid opening.
The 2nd reason for the fast preheat time is that I'm using a real pizza stone now (from Sears for $12) instead of FB or QT. Why? Well, it's mostly b/c it's in one piece instead of multiple pieces. This stone heats up faster and transfers heat much faster than the QT or FB. To compensate for this, I load the pies at a lower than normal hearth temp.
Now let me explain. I did just say I loaded the previous pie at 700F right. Well those pies are 75%/25% pastry flour/AP flour meant to be loaded at a hearth temp of 850F. If I was cooking BF or HG flour I would loaded the pies at maybe 550, 600 max.
I did away with the FB b/c the MBE has a low dome and the FB was too thick doming the pies. I did away with the QT b/c the pieces were shifting too much with me turning the pies frequently.
I think you can tweak yours to lower your preheat times but it may very well be just the nature of a bigger kettle. And besides, my latest thought is that you don't want a higher hearth temp than 600F if using BF/HG flour. And not that the flour can't handle that but b/c the flour benefits from a lower cooking temp and a longer bake time. On yours, you can try this. Once the hearth temp reaches 600F, I would load the pie and turn down the burner about 30-40% or so. Plan to cook the pies for 5-6 minutes instead of 3-4m like I recommended before. I am doing things much different these days. I believe a BF/HG flour dough benefits from a relative lower hydration ratio rather than higher even though by nature it attracts more water. The excess water of a high hydration dough will only prolong the bake times or give an undercooked pizza if using a short bake time. Just some thoughts is all.
This longer bake time should allow the proteins more time to bake and drive out more moisture. If I am correct, you will get a better pie than before. Even baking at a lower temp should save you some preheat times. Also try turning the lid during the preheat time or add a lip to the dome to see if that helps. At this point I'm more just reporting what I see going on rather than having all the right answers.