I just 3D printed a case, made by importing the outline of the board into Fusion and messing with it a bit. It's not as low-profile as it theoretically could be, because the shortest standoffs I had on hand were 6mm, but if you have shorter ones you could easily make this thing way smaller.
You can find the files in the repository in STL, fusion, and STEP formats.
You will need to print one
peridot_plate.stl normally and one mirrored, so that you have a plate for both
the left and right halves. Then, you'll either need to print
peridot_base_full.stl (if it fits on your printer)
peridot_base_left.stl and one
peridot_base_right.stl and glue them together. They aren't too hard to line
up, as long as the surface you are gluing on is glue-resistant.
Other than 3D prints, you will also need 12 m2 screws and 6 m2 standoffs for the build, and probably some rubber feet. I'm currently working on coming up with a solution so that rubber feet or a 'laptop adapter plate' can be swapped on and off of the case, but that's not done yet.
I don't think this case is the best that it could be, but it works.