The cheap plastic box I ordered on Amazon took quite some time to arrive... until I realized it was shipped from China.

The size is just perfect. I cut a few holes, one for plugging in a USB-C cable (to allow direct reprogramming without having to take everything out of the box), one for the cable from the air conditioner, and I added a small light pipe so the microcontroller LEDs could be seen. Everything was secured using my best friend number 2, hot glue.

The final result looks like this (the case held with Blu Tack):

I may redo the cable that connects to the air conditioner motherboard, but for now, I'm happy with how it looks.