MetroMPG, IIRC, the twist that you see is supposed to be there to make the rotation smoother. It has to do with the magnetic feild being pulled less like a pulse and more at an angle. They do the same things with generator windings.
Personally, it is WAY more dificult to rewind your windings yourself than have it done. It can be done, I've rewound one generator rotor( 4 pole) and never again. If you are going to try it yourself, before you buy any new wire, try unwinding it, by hand, trying not to chip any more of the laquer off the wire. Test some of the windings to make sure they are still good( no grounds or opens), some will be, and see if they are still good after you are done removing them. A meger is a good tool to have when attempting this. Of course, it can also be used to burn up windings as well.
Best of luck