I didn’t feel like getting into woodwork with high chances of messing up, so I gave Lego a go (actually a cheaper Lego-alternative, that might be even better because the pieces snap more tightly together and are harder to separate).
I was planning on glueing the whole thing with MEK, but thought that it would still be too prone to break and not be strong enough to hang on the wall. So for now it’s literally a Lego frame.
The spidey-cabin-element is meant to hold the Raspberry pi in place, since then we put the pi in its case, so it needs a bit more room. Good thing about Lego: I can flexibly change it.
I used lego pieces sticking out of the frame and into the box to hold the screen in place
And built a one-lego-stud-wide slit (8mm) to hold a 4mm mirror in place.
Seems to work well so far.