Tom,
I think attempting to unwind some of the HV coil is worth a try. If you can expose all of the HV winding, you might then be able to localize the shorted turn by seeing where it gets hot.
And the transplant idea might work, but it would be tricky to find one that fits mechanically ad has the right number of turns.
My coil winding machine was mad by the George Stevens Co, and is a very sophisticated device. It has interchangable cams and gears to set up the coil width and the ziz-zag winding pattern (also known as a universal type winding). Here is a photo of the machine winding a HV coil, like what you need.
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John Folsom
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