Trouble understanding these deformers on a rigged character

[sonicxl09]

I can't seem to grasp how to use the deformers in this character model I've downloaded.
The easiest example is this-

This is what the character's hair normally looks like.
But when I start posing- for example, by moving the neck, 
this happens:

I thought it might be a case of double weighting, and when I checked said weights, there is more than one skin cluster effecting the mesh.

I've been combing through material for hours, but all I can find are cases where the person has joined each new cluster to a different joint.  Whereas this model seems to be made with the intention of using both clusters to influence the same joint.  Even then, removing or repainting weights on either of these clusters seems to pull the mesh even further, making me think it has to be something else.

In which case I'm not sure how to fix this.

Another issue I've had relates to these deformation groups:

They cause similar issues, where meshes will deform as though they are attached to something else, unless I turn them off.

I have been trying for about two weeks to find an answer, I have other projects I am working on this month, so I would greatly appreciate any help.
I've attached a zip with the project file inside.
Thank you in advance.

[mcw0]

Years ago I played around with multiple skinClusters.  And came to the conclusion that for most cases, it was more trouble than it was worth.  That being said, in your case, the skin weights for skinCluster1 looks good for the selected joint.  I would try turning off skinCluster2 and see how things look.  Both skinClusters have the same joints displayed in the paintUI.  Why you would want the exact same influences on 2 skinClusters is beyond me.  I would think the second skinCluster would have different influences.  Otherwise, you'll get double transform type deformations.