Bind Skin to Object Being Deformed by Proximity Wrap

I have a character’s scarf attached to his shirt using proximity wrap and it results in exquisite deformation along the side of the neck; however, I’d like to add some additional control for animators by rigging a part of it with joints.

  1. Applying a skin cluster before/after the proximity wrap is not giving accurate results (it is either ignored or applies double/weird transformations)
  2. Trying to blend them together via a blendshape results in undesirable effects when rotating regardless of deformation order
  3. If I attempt to blend the vertex memberships between skinCluster and proximityWrap, the model’s normals get messed up and the mesh looks black when looking at it from many directions.

Is there an official way to use these deformers together, or am I attempting to use these in a way that they weren’t intended? How would you guys tackle this task?