Wow, I can barely imagine trying to manually wind a coil about a millimeter in diameter ...
They must have fixtures or machines for doing this at the factory. But anything can be done if you're determined, and it might be an opportunity to improve performance ...
As best I can tell, it looks like the electrical contacts are made through the ends of the coil bobbin, but there is a feature under the coil that I can't see clearly ...
Of the 25 atomizers I've purchased, all but one are still working after a year, and that one was destroyed by me in one of my early re-wicking attempts ...
With care, the barrel and spike could last indefinitely, and I don't know how long the stainless steel wicks last, I'm still recycling all of them. I squeeze the barrel to make it just slightly elliptical when the press fit starts weaken ...
RogerWilco, if you can successfully rewind a Type A coil, and perhaps get a better vape, I would salute you and hope for a video to learn your technique ...