I decided the solution might be to make wooden boxes for support. But I came across a couple of pieces at the local Goodwill that were the right size and might work.
Meanwhile, I cut out three 8" squares and the four sides for each and will do it the slow way: let them set up to leather hard (the clay is stiff but not dry) and join the pieces together with score and slip.
In the past, for the arch tiles and birdhouse tiles, I've always thrown the sides on the wheel as a ring without a bottom, let it dry slightly, then altered the shape, put it onto a slab and joined the two together. I never got the sharp right angles on the corners that I'm trying to get with this new method, and it was difficult to throw each ring on the wheel exactly the same size for a set of tiles.
I have another idea. Do it like I did the first one at the top, but support them with 8" x 2" pieces of wood or something stiff, then tape around the corners of the supports to hold the piece while it dries, checking it occasionally to make sure the sides are staying straight. I'm trying to avoid doing it the slow way but still get the tile I want.