internal contouring with cnc

Hello - I am an amateur flutemaker, working in wood and delrin(a
polymer), and I have been wondering about the possibilities which a
CNC lathe might offer for creating the bore of the instruments. The
bore profile of wooden flutes is rarely a simple cylinder, and varies
from flute to flute, and is one of the most time consuming parts of
the whole job. Small changes in bore profile also have a crucial
effect on the qualities of a flute. The traditional method of making
a flute is to take a wooden blank of the correct size, drill a pilot
hole and then use a specially constructed reamer in the lathe to get
the final internal profile of the bore. Problem is - you have to make
a new reamer every time you want to modify the bore profile - which
makes prototyping a very slow business. So I have been wondering if
there is some technique available(not too expensive!) using a CNC
setup and a controlled adjustable boring tool which I could program
to cut a given bore profile, which I could then easily when I wanted.
This would eliminate the time and effort involved in making new
reamers every time I want to experiment with a new bore contour. So
there it is - any help or suggestions would be much appreciated.
Thanks in advance.
gerry