Unfortunately checking the Bend option for the head object didn't make a difference (it was originally unchecked.)

Here are the available parts of the firgure: Head, Body, Control (an attached control prop), lTopBraid, rTopBraid, lBraid1, rBraid1, rTail, lTail. Here is what I tried that did not had any effect:

Select Head and create magnet
  Add Body to deformer
Select Body and create magnet
  Add Head to deformer

I do appreciate the suggestions though.