Originally Posted by
pablopepper
I would suggest getting some wood veneer and playing with layers. Wood veneer is usually 0.6mm thick, so start with a piece about a half to two thirds of the length of the pocket, place it at the back of the pocket, clamp your neck in again and check action. If that's not enough, cut another piece half the length of the piece before, stack, clamp and check again. Repeat until mostly happy.
When you are done, glue the stack of veneers together, flip it and give it a rough sand to smooth the layers out a bit. This should give you a workable shim with little to no power tools used.