Before you buy one I'd have a look around at what types of complex wire reels are out there as most places seem to have stopped selling them or drastically reduced their range to just one or two types. I always bought my wire reels from Vape Club but this is the only decent one they still have.
Coilology Multi-Strands Fused Clapton Wire 10ft Reel
This coil tool kit on Amazon is the closest I could find.
Coil Master Coiling Tool Kit
Your little coil winder tool is good enough for thinner plain wire but for thicker complex wire being able to anchor the wire makes it much easier to wind your coils tightly enough.
All you need is the red handle piece in the photo with the 'Magic Wire CW' writing on it and the right size rod for the size of coil you want to make.