It seems like a bug to me. Whenever you have an opacity map on PBR hair and enable Toon Shader, the value of Specular and Glossiness sliders are "leaking" from a Traditional shader and influence PBR.
In PBR/DHH those sliders are not available (grayed out) and should NOT have any influence. But with Toon shader enabled, they apparently do. That is why you cannot do anything to stop that shininess.
So switch PBR or DHH shader to Traditional on Hair, scroll down and set Specular and Glossiness to minimum.
Then you can switch back to PBR, or DHH. Or leave Tradition (which is what I would do).
The other way to fight that hair problem is to set Self-Illumination to max. It would effectively kill all specular (just have to remember, if you decide to render in normal mode, roughness/specular would not be in effect).
Finally, hair opacity. It's good to have detailed opacity maps for the hair in normal shader. For the toon shader however, it would be more natural to set Opacity maps strength to minimum.
And YES, Fibermesh (pixel) hair is not a good choice for iClone. They do not render well in any mode (except Iray).