I would stick with the nylon tread as it will protect the wire, the thread is only a very crude ( but effective) traverse feed. It might be worth making it over long and supporting it on both ends, that will solve the run out and give you the option to wind 3 pickups in one go.

Started a winder project a while ago but didn't get to cnc,ing it. Used an aurduino to set motor speed and count coils. Have you looked at ink jet printers? They often have small steppers connected to plastic thread. Might save a bit of work.

Off topic but have you thought about wire tension? From what i remember it is fairly critical to the sound and therefore repeatability.