I just ran into an instance where in Volume mode, the wrap is working well. Except for the mesh borders. When I switch the wrap mode to Surface, the mesh borders were perfect but the interior mesh areas were less than ideal. So why not have an option to do a falloff over a user definable distance from mesh borders?
As of now, my workaround is to duplicate the wrap deformer so I have 2, one set to Volume and the other Surface. Then I apply a blendshape and paint weights. Not very elegant.