First try lowering your bend resistance. Possibly the root stiffness also since this is a hat. You might try increasing the vertexes but use a small group for that because this will up your sim time greatly.

You can also try using the morph brush. I don't remember if it will work on draped hair. If it doesn't, you can use Cage's bake deformation script to back the draping before using the tool. You might also want the sticky addon that prevents the morph tool from switching what is selected. It works better that the shift button when using the morph tool. I don't remember who wrote it though.

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