A trick with hair is to insert a second hair model/prop, scale it semi-flat along the z-axis and/or the x-axis, and then position it until it matches up with the hair on the figure's head.  Positioned carefully, it can give the appearance of the hair hanging upside-down.  You will probably have to play with the morphs in the hair on the figure's head as well.  Perhaps make parts of the hair on the head invisible, if it has zones.

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