Animation and import scale

I am re-using the same skeleton for all my characters.
Some are large others are small and I define their scale inside unity with import scale.
The problem arises when I use the animation of the 1:1 scale animation library on a 0.4 character
The root hip animation isn't scaled and so I have a character that's walking in the air.

See the hierarchy is a typical : root-hip bone-rest of the body and the skeleton is animated by a control rig that's not part of this hierarchy.
Normally when the bone rotation and hip position get baked, the position animation of the hip is relative to root, in such case, scaling root via the scale import inspector should yield to walk animation that's properly scaled.

So what is the proper worlkflow to handle multi scale character with common animation library ?