That really is the cheapest way to go.. as far as looks, not so great. I also have a concern about dimensional stability. Once the heat gets up there, you could be seeing a lot of movement with this approach. Sagging, warping, twisting, all things you don't really want when you've got an 800+ stone + a dome balanced on top of your LBE.
Brian, a curved piece of de-galvanized steel or copper flashing will be very dimensionally stable, as long as it's not too lightweight of a gauge. A thin sheet of metal, on it's edge, has considerable compressive strength. I also have been talking about supporting the lid OR the stone, not both. With the stone sitting on the flashing, you really don't need the lid.
You can also take twice the length of flashing that you need, fold it in half and have two concentric rings. This would be especially good for copper because it would give you a sandwich of air to act as insulation.
Another idea that came to me is placing two strips of flashing together, folding over the last inch, then folding that inch in half again to make a union. When you separate the two strips the union will be 8 layers of metal thick, and, when on it's side, give you even greater compressive strength. You could, in theory, place these unions every few inches along the C.
When you buy the flashing, you won't be able to get a strip that's (2/3 to 3/4 the circumference of a 22.5" circle) by 4 or 5" (the approximate height you'll need), so the excess flashing can be used to double the ring or other kinds of fortification.