Well, I'm no guru, but I'd also suggest Dave's idea above. Try to make the string in the spline modeler and animate the location of a bezier control point along the 'string' so that the bend moves from one end to the other. Then have the spline object move in the assembly room so that the bend's location stays in contact with the edge of the hole. This is just off the top of my head, so I haven't tried it.