The PCBs from @Elecrow arrived today, so it's time to assemble the new version. There were absolutely no surprised, and everything seems to be exactly as it should be:
The display aligns with the silkscreen properly now, and the traces for the buttons no longer get in the way of touching them, so there are no misclicks.
On the back there is room for your name:
Unless I'm missing something very bad, this is the final version of the device. Now it's just a question of the software for it.