I'm of a mind to go the CNC route as well, altho I think a 4-axis machine is necessary. Once you have your stock blank on a spindle that can rotate under the cutter, you've attained the required cutter movement over the stock.
The challenge, IMO, in cutting on a CNC will be programming the machine to take progressively lighter cuts as you get closer to final dimension. When you're in the middle of the stock, there's substantial flexing and you have to have a light touch on the cutting pressure to avoid deflection of the stock. CNC mills don't know what "light touch" means, so you have to program it in.
BTW - making a stock duplicator shouldn't be difficult. The big units are just made with some I-beams of steel for the base, then some round linear ways for the pantograph upper. There's no rocket science involved anywhere on the machine.