This would work better if you used a long pin, shaped like a nail, and stacked thin lamination pieces on it. The smal end could be peened over like a rivet head to hold the stack tight. The use of laminations will greatly reduce the heating.
The laminations dont need to be special electrical steel in order to help. If you want to make one on the cheep and see how it works get a chunk of a junk refrigerator. Then you are going to need a way to punch your 3/8" diameter discs, with a small hole in the center.
The stack will need to be very tightly compressed, no gaps allowed. You may need to even remove the burrs from the edges and center hole in order to get them to stack tightly. You would porbably want to press the stack tight before you fasten it.
One more thought, instead of using masking tape try to find some mylar or Kapton tape. I have some Kapton film (no adhesive). They are much stronger and will resist wear better.
It would also help (reduce noise, increase life, improve cooling) if you glued the windings together. An epoxy would be a good choice. Coat the core with a thin layer and start winding. Add a thin layer of adhesive over each layer of windings. Make sure that it is all cured before you power it.
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Corrosion never sleeps, but it can be managed.