I said earlier that I planned to use a double-gang electrical box to hold the smarts. That was because things just won't fit in a single-gang box. For a different project, I went sight-seeing in the hardware store for enclosures. I found something that I had overlooked before.
Here it is:
Those mounting tabs on the bottom corners are easily trimmed off. The cover is not a double-gang outlet cover because this box is intended to be used for junction points for wiring. The cover for it is mostly a big, flat, blue square. This should give me the option of mounting the screen horizontally or vertically (or, if I'm really wacky, diagonally).
As I mentioned, I used this for a different project, and the result was satisfactory for something that will live in an out-of-the-way place.