I decided to make one last attempt at the case and the button caps, and that hopefully will be final. This time the PCB stays the same, I'm only laser-cutting a new front plate. I made everything fit on a single 100x100mm sheet of 2.5mm acrylic:

The D-pad cross is a bit larger and has rounder corners, the fire buttons are round. Both have a cut in them for springiness. The middle layer is split in two, to fit in the sheet — I would love to put one more screw in there, but that would require a change of the PCB, so no.

I will go with the regular 6x6mm tact switches with 6mm high stems, however I will try to find ones that have as small actuation force as possible, to make them softer and less "clicky".

While I wait for the order to complete, I will now need to work on the website for the project, and then try to find a distributor willing to sell it.