The toughest part of the build is digging out the concave back and thinning it to the right thickness
 After shaping the outside like you want it you turn the piece over and begin hogging out the inside. |  I use a forstner bit that has had the point filed a little shorter. Set the drill press so that the tip of that point stops just at the desired thickness of the back. |
Then, when you have hogged out all the wood possible grind down the rough spots with a disc sanding device on an electric drill. You sand away wood with a coarse grit (36 grit) sand paper, until all the holes have disappeared. Then you will know that your back is at the right thickness.
This is a dusty tedious job. use a new sharp sanding disc and finish with a finer grit, but hang in there. It is the only way that I have figured how to make a concave hollow instrument back. Be sure to wear a dust mask.