It's very similar to LBEs that have been done before, with a few minor improvements.
Basically, I removed the Weber lid from the picture. It's too tall to effectively radiate much heat down onto the top of the pie and hanging false ceilings is a hassle. It's easier just to make a ceiling out of a large round cordierite stone. This stone ceiling sits on a curled strip of galvanized steel flashing (not pictured) that goes around 3/4 of the outer circumference of the grill.
My flashing is basically a DIY version of the Kettle Pizza
insert mentioned above, except my flashing only mimics the bottom half the insert where the hole is. It also has no handles. The pizza kettle insert, besides being costly, is way too high and only compounds the ceiling to pizza distance issue.
The height of the flashing might take some trial and error. The way I'm picturing it, one will launch the pizza with the flashing in place, so you want it tall enough so that the pizza doesn't touch the ceiling, but not so tall that it gets in the way during the launch. Right now I'm leaning towards 2.5" above the hearth. From what I can tell, they sell galvanized steel flashing from Home Depot and it should be lightweight enough to be cut with tinsnips, but, on it's edge, it should be sturdy enough to support the ceiling.
A round 19 x 1/2" cordierite stone shouldn't be too difficult to track down, but a 23" cordierite stone could get tricky. A 23" x 1/4" round steel plate would probably do the trick as well, although that too could be difficult to find. If all else fails, get a 23" square 1/4" thick plate.
The sizing on the thin steel deflector boils down to where it ends up in the grill. Ideally, you'll want it pretty close to the hearth so it can be close in size to the hearth. If the deflector doesn't shield most of the hearth, you'll see very hot edges on the hearth. 2.5" to 4" from the hearth should do the trick. I'm not in love with the price, but something like this should be perfect:http://www.wasserstrom.com/restaurant-supplies-equipment/Product_421222
The nice thing about this tray is that the edges curl up, so, if you wanted, to you could fill it with some sand like some LBE folks do. It will most likely warp, but it shouldn't warp so much that it can't be used. Although I'm not in love with Pizzahacker style perlcrete ceilings (you really need some
thermal mass in the ceiling), you might be able to get away with a perlcrete deflector. Maybe. The most important thing is to avoid aluminum, both in the deflector and anywhere else, because there's always the possibility that you'll reach aluminum melting temps.
One other aspect regarding the deflector is that it might work a bit better tilted towards the side the gap.
You might be able to salvage the handle from the original weber (or another grill) or you might be able fashion something out of steel bolts and wood. The other thing I was picturing with the lid is, when you remove it to launch the pizza, you can rest it on whatever steel flashing is leftover.
Lastly, the lazy susan that I'd go with would be this one:http://www.lazy-susan.com/catalog-product.php?p_ref=258591
as it, from the photo, appears the be the model Mike (Essen1) has used in the past.
I tend to be a very thrifty modder, and, although this is a bit more than I normally like to spend on these sort of things (in the $150 realm), the mods involved should all be very simple and the end result should pump out some great pizzas with fast bake times, possibly even Neapolitan times.