I'm thinking what you are thinking - just use the regulator or in-line valve with fine control to dial the flame. I'm finding that there are times when I just want to dial down the heat and let it idle between pies. I haven't done all the research yet.
I've tried a bunch of different deflector types from top mounted (slipped under the upper stone) to baking stone level, to deflectors mounted near the burner (control the flame profile from start to stone to top). I'm not saying that I've exhausted every option, but I haven't found a deflector that is compelling.
At one point I was getting too much browning of the cheese, so I slipped some stainless steel under the top stone. The idea was based on 'really good science', reasoning that the hot, high emissivity stone, was charring the cheese. (Remember the toast experiment?). According to the calculations, the radiation from stainless is significantly less than stone. Indeed that seemed to help, although the stainless turned almost as black as the chassis - I guess stainless is more of a marketing term.
As I've mentioned elsewhere, I've started working the pie and flame much more than before. In short, I set the baking stone temperature, throw a pie, give it 30 seconds to set, then use a turning peel to keep an edge of the pie near the flame. I use a standard HD rotisserie, instead of the stock BS rotisserie. Besides the added durability, the HD rotisserie turns opposite the stock BS unit, making it easier to keep the edge of the pie in the flame.