Thanks to everyone for so many great replies already. The pieces are used to make oboe reeds and the current method of gouging or removing the material is outdated, imprecise, and overly troublesome. we basically use a small manually operated "machine" to slide a curved blade across the piece, removing one strip at a time until it get to the desired thickness. Google "oboe gouging machine." These machines are still quite expensive, from $1300-2300. Then we need multiple machines to produce a selection of results (the thickness etc. has to change with the weather seasons).
Barring how to hold the piece down to make the cuts, would a CNC machine be able to cut precisely enough so that my end result is an exact thickness? Starting with something about 2mm thick then taking it down to .60 mm. I imagine this would require a really small and fine bit? And is there a way on the programming to vary exactly how thick it will cut at exact points if the dimensions of the starting blank are programmed in? My dream, which may end up being farfetched, is for a machine like this to gouge the pieces not only precisely, but then also allow me (on the computer program) to alter exact specifications of thickness and gradation etc.