The process of looping and then twisting the wires from a coil is called skeining and is used in proper coil winding alot. I taught fill alot about coil winding
In practise leaving long pieces of wire dangling from coils for later skeining can be a recipe for disaster, you have to be very careful not to snap the wires. I had considered adding a skeiner to my winder such that two would wrap the wire around two hooks before beginning the wind, then one would spin to skein the wire. This wire would be stowed in the windiner head (wrapped around say) and the coil would be wound. Then at the end with the coil still in the winder the same process would be completed for the other wire. I just never got around to it.
Billy, the point of is being multistrand in our case is just for flexibility, strength and tunability, you can make wire for all occasions.