Hello,
I played with the shaders a bit. I like what happens when you replace the noise node by
a clouds node. This gives  bigger areas of colors.
The hair node seems to be very special, the color is mainly driven by u/v, but
from the hair root to hair tip, it has some additional parameter you don't get 
with other nodes (or, in other words, without the hair node, I was not able to 
obtain which changes color from root to tip.)

Carodan, your settings are very aggressive, I also reduced the hair thickness,
but only to 0.6 for root and 0.3 for tip. Your renders look very good, which proves
that the additional reduction is worth it!
I also double the number of hair segments in general, that gives smoother
bends.

It is possible to use an additional blinn or anisotropic for hair, but with too much
light, the hair easily looks washed out / grey then.
With even tiny bits of translucency, the hair did not look good any more.

Best regards,
  Michael