I'm curious if it was a problem tensioning the source wire. If allowed to slack, there are problems. In the past when I've done this I had help or used my spare hand to put two almost 90 degree bends in the wire (without actually making a full angle). That and the friction from my fingers helped. I know I've seen wire tensioners before too. Not sure how they do it on the tape, but anything that keeps tension should help in winding. The hard part for me was getting it to spool up evenly instead of bunching in the middle or against one side.
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Experience is a hard teacher because she gives the test first, the lesson afterwards.