That might actually be possible in the fire if flexible e-paper becomes a thing, just need to figure put where to put the electronics
Edit:
You could also just set up a regular e-paper / e-ink display in a frame as well and have it display a calender and just integrate the electronics into the frame
Yeah, the way they work is based on your eyes seeing two slightly different images because of the difference in their angle to the prisms. By having one image, the full name of the month, shown through the widely diverging angle made when you are closer and a second image, the short version, shown when the diverging angle is more acute you could have the two options visible. Everything in between would be a bit of a crapshoot though, with a muddy mix of both. Your brain likes to figure out images that can make sense, but text can be very weird and in situations like this it would probably be very muddy and more distracting than cool.