OK, the power of procrastination is immense. I already made the backplate. Started by cutting a rectangle from a piece of sheet metal. Who needs laser cutters when you have a hacksaw?
Next, I taped the two plates together and drilled the holes, then did some filing and dremeling to make the metal plate smooth and to round its corners. The result:
I used nylon spacers to connect the two plates together, cutting off the excess pieces of the bolts.
Next up: wiring.