I think AusCan's suggestion may well work, and is easy to bench test. But I would be a bit worried about the wire end that's inside he motor case and unsecured. If that makes contact with ground, it could get ugly.
If you are up for it, take apart the motor end and see what's going on in there. You might even spot an easy way to reattach the wire and stud, or at a minimum insulate the wire end, then try the AusCan reverse wire trick.
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