Your burner definitely won't be overkill - I believe the Bayou is even more powerful than that, and as you said, you simply don't turn it up full blast
You are definitely asking the right questions - I think that the internal construction of the lid (oven ceiling) and the heat buffering are the 2 keys to getting great results w/ the LBE because you need to balance the top heat w/ the bottom heat and this can take some tweaking
I never did try the stone in the lid, mostly because of the extra weight so I don't have a comparison, but I started w/ just the ash-catcher and found that it worked ok but that I wanted more heat directed to the top surface of my pies so I constructed what several have called a "vortex generator" - basically a way to direct the heat flow back down toward the top of the pie instead of just rushing straight over it and out the side vent - this feature was definitely an improvement - you can search this forum for the different ways that people have done this - mine was basically just a thin perforated piece of metal that I bent to direct the airflow in different directions
It also makes a big difference how much oven space you have between the cooking stone and the ceiling of your oven - since heat rises, this will drastically vary the temp. that the top of your pies get exposed to
I think the steel shelf w/ vents is a good way to go if you have access to the tools to make it - I would actually be interested to hear how you will make it, since most people have said they have had metal shops make them- I use a piece of scrap metal that more-or-less fits the shape since I don't have tools to cut thick metal
I don't think you will need any other stones or buffers besides this plate - I have been using a 5/8" kiln shelf for a while now - it is indestructible and it really absorbs heat much more than a typical pizza stone - it does need some buffering, but if you buffer it too much, it takes forever for it to heat up - I tried only a thin cheapo store-bought stone underneath the kiln shelf - no metal shelf or other buffers, and I got impatient waiting for it to heat up - it buffered too much
Having said all of this, since the LBE is a DIY project, there are multiple variables that makes everybody's project a little different and everybody's techniques and desired results are different, so at the end of the day you just experiment a bit until you find your ideal setup - it's what makes it fun!