Hi Jake
If the back of the phone was attached to a thin hinged door then closed the phone would be face down when the door opens it would be revealed. face up at the angle you require
You would need a stay to hold the door in position, like the stays you find on a suitcase. with a bit more design work the stay could be eliminated
The door itself could be a piece of say 2.5mm aluminium veneered or painted to match the guitar.
That should fit easily within your 40mm body.
Looking at your sketch there is not a lot of space around the edges of your phone. You may have to modify the shape of the body or use a smaller phone.
Is it going to be a synth app or are you going to use the phone to display music or lyrics?
Regards
John
Edited By John McNamara on 26/08/2015 15:32:41