Attach the monitor with glue to the mirror?
One thing to note: I noticed that the mirror coating on my magic mirror is very delicate. I am not sure if other people have ordered from TAP Plastics.
Adhesives seem dangerous as it could rip that backing of the foil-like mirror coating right off!
I completed my box construction yesterday. My solution to the monitor-is-smaller-than-box problem was to build an internal bracing system using a couple of channels for the edge of the monitor. It sounds more complicated than it is.
Everything in place: