I've thought about this for a while (for my own project) and I think what I'm going to do is:
1. Using black matte board (with a black core) cut a rectangle to fit the entire space
2. Layout both the horizontal and vertical holes you will need to cut to see the monitor in both positions (the white lines in the attached pic)
3. Cut out ONE rectangle (probably a square) out of the matte board using the vertical and horizontal rectangles as a guide (the red lines in the attached pic)
4. This is your bezel.
5. Using another piece of matte board which will go directly behind the piece you just cut (by like 1/32" or something really small so when the monitor rotates it won't rub the back of the bezel), frame out your monitor so that you will not be able to see through the bezel and this frame when you place the monitor in either orientation. You won't need anything on the sides but you will need to add some thickness to the top and bottom - make sure the frame and monitor have enough room to rotate.
6. Get a piece of gray tinted glass to cover everything. Even close up you won't really be able to tell that there are two pieces of matte board in there and the illusion will be complete.
Does this make sense? I hope so because this is exactly what I'm going to be doing when the time comes...
