I'll use the template and Router to clean up the edges and bottom, but I took most of the material out with a forstner bit on the drill press. I want it 21mm deep so the the surface of the body comes up under the over hang of the fret board. To get close, I set the depth stop to 15mm from contact.
Result
Then went back with a smaller forstner bit and took another 4 mm or so, got closer to the corners.