dan38711: Coils that I have wound very carefully by hand agree almost perfectly, whereas sloppily wound coils deviate significantly.
Where on this spectrum from perfect to useless do ordinary machine-wound coils using simple turn counting fall? Would it not be sufficient to machine-wind one layer of the coil, manually pause it at the end of the layer and note the number of turns, and then program the winder to use the same number of turns for the other layers? This could be a very simple process if your CNC controller was designed to support it, and without needing any exotic measuring techniques. It seems unlikely to me that you would need to deal with variations in the wire thickness within a single spool, and I expect that once you have got it set up for one coil you could then continue to wind multiple similar coils with the same settings.