A few thoughts.
First, making a burner may seem easy enough, but there are major safety issues involved. There's also, I believe, a great deal of difference between the burner making videos on youtube and the kind of BTUs that you're going to need for this. Just because the flame is closer to the pizza, doesn't mean that the BTUs can be considerably less than a traditional LBE setup. A high BTU DIY burner could involve more holes, bigger holes, a higher pressure valve, or all of the above. I have no idea. I am relatively certain that as you move away from simple low BTU burners to high BTU, safety becomes a bigger factor. Proceed very carefully and do plenty of research.
Secondly, based up the dimension of the stone in your diagram, the stone will be 14". For Neapolitan pizza, you may settle on something smaller, but you will want the option for doing 14" pizzas and launching 14" pizzas on a 14" stone is close to impossible. If you are going to take the time to do this, I'd really see if you can track down a larger weber. Everything should fit a lot more comfortably.
Third, I think you're going to want to point the holes slightly towards the pizza, at an angle, rather than pointing straight up.
Lastly, the arc of the burner doesn't need to be any more than 180 degrees. You don't need to fill that much of the circle with burners- a semi-circle is sufficient.