I spent another hour tweaking to correct the worst bits and it looks more natural, even though the skin tone is a bit off compared to the references... Only one wider spec lobe this time : GGX does a very nice job as usual.
New environment : Winter Forrest (recommended by Christian Bloch). It doesn't have much dynamic range but it is quite neutral. Very Game-Of-Thrones-ish too.
I had to improvise a bit for the eyes (with a ramp for now), but it's good enough for today ! What sells them is the meniscus and the eyelashes, anyways... :-)