Hi !
I also work on this project. We've made a little bit more investigation yesterday and actually we managed to find where the problem is coming from : Z spacing.
This character has more than 250 slot with each a sorting index, index that is multiplied by Z spacing in Unity to avoid Z fight. In some animations (like the one Moinelle showcased in here video), some pieces are doing huge index "jumps". For example passing from 5 to 240 in order to be first in front of given slot and behind it a couple of keyframes later.
In our game Z spacing is set to -0.001, so for instance a jump of 200 can create a significant offset.
If we reduce the offset to be -0.0001 (10 times smaller) or if we avoid doing big index jumps within the same animation, the problem is solved.