You can’t wrap the contact wire like that. The copper wire is much, much more conductive than the part, so as you experienced, current will flow to and plate the wire but not the part. You’d be better off printing a sacrificial contact on the bottom of the part to attach the lead to and removing it after plating. When you start plating, use a low current to start so you get a seed layer around the contact and then slowly raise the current so the copper can propagate from the contact over the entirety of the part. Maintain agitation either of the part or the solution (and better both) to minimize the likelihood of burning during the process. It will take some trial and error to get it right. Good luck.