Sure, thing, Art.
Actually, it just occurred to me today, that, since the ceiling tiles aren't contacting the food, you can use regular glazed tiles- preferably black with the glazed side down. You could also put the glazed side up if the base clay was a dark color.
I'm attaching my most recent grill setup recommendation below.
After so many people are getting broken quarry tiles, I'm beginning to sour on them a bit. They don't cost much, so you can certainly try them, but I'm leaning towards firebrick splits or fibrament. The splits are 1.125" thick (generally) and will suck up a load of heat and use a lot of fuel, but on the positive side, they'll stay hot for quite a few pizzas.
If you do end up with quarry tiles, thickness is not a huge concern. I guess 1/2" thick might be a bit better for the hearth, because of the greater thermal mass, but 1/4" probably wouldn't be the end of the world. When it comes to quarry tiles, you generally get whatever you can find, as they can be hard to track down. The more important dimension is width. I've never tested this fully, but I firmly believe that smaller tiles are both physically and thermally stronger because they can expand and contract as individual units rather than as a whole.
The fibrament grill stone is a standard thickness- 3/4".
One important aspect of the grill setup is to use a relatively massless method to support the ceiling. If you add anything with thermal mass it will suck yet more heat out of already heat greedy system. Do not use firebricks. Aluminum flashing should be perfect and can be easily cut with tin snips. If your stone is round, you can cut the flashing into a C, but if your hearth is square, you could probably get away with squaring the shape of the flashing a bit. Just make sure you bring the flashing around the front of the stone a bit so the ceiling has 4 relatively stable corners to sit on. The ceiling could be heavy, but, aluminum, on it's side, should have no problem taking the weight.
Btw, this is all predicated on the grill having enough BTUs to hit 650 pretty easily. These days, I think that's most grills.
Also, just to be clear, this setup is for NY style pizzas only (4 minutes and up). If you want Neapolitan, you either have to have a grill with an infrared burner, a carefully crafted LBE (and a lot of luck) or a 2Stone inferno.