OK, render isn't finished, but the head is:) 

So, I used select to remove the white background from the texture, and duplicated the "texture part" 2 times moving the lower layers a little to the left and right. Then I painted the background a solid color sampled from the darker part of the hair texture and that does help it. I have actually done this before with plants' leaves, don't know why it didn't occur to me when it was hair.

That works too with texture-filtering set to crisp. For those who hate texture filtering, in this example, her hair was pixelated without it, at least where the strands fell across her face. I'll post a few of the renders to show the problem and fixed results.