Thank you Harald !
For characters where we are controlling the bones by code, we will work on a special shader as suggested.
For the other ones, we tried to export as frame by frame animation, and then make a new spine project using these frames and re-export as bytes. That way we end up with a frame by frame animation with skeleton data to use in unity, and we don't have the overlap problem anymore. Cherry on the cake, the performance gain is about x8 !
note :It would be great to have the option to export a frame by frame animation with skeleton data, without having to create a second project.
Thanks for your help!!