One approach is not to have an independent head, then you can do anything you like with the layers and get it all right.
But if you need the head independent, you can do it, but what you have to do is have an independent layer for say the arms and hands which is in front of the face layer. You can then attach those independent arms to the shoulders. Anchoring independent layers does not care the depth order— only that they overlap. However, depending on your artwork, putting the arms in front of the body can be a pain as well. For example, it works well if your arms are flat colors. If you have texture on the arms (e.g. a patterned shirt), its more problematic.
On another scene I introduced a second puppet for arms and hands and did a close up on the face so you could not see that the arms where actually not a part of the same puppet! (They went out of shot to the sides.) Sometimes its easier to be “creative” about camera placement than fix the puppet. (I know that is not always an option, but worth considering!)
The hard ones are where you want the arms *sometimes* in front and *sometimes* behind. That can also be done using two sets of arms and triggers (you hide one set of arms or the other). You make both sets of arms Independent. Its a pain however as you have to duplicate any hand positions, draggers etc. So its possible, but more painful.
Oh, my other favorite trick sometimes is to create two versions of the same puppet with different layers or different indepedence, then flip between the puppets at particular times (just hide one and reveal the other). E.g. does the head have to be independent at the same time as the hands go in front of the face? Can you cheat and have two puppets - one with head independent but hands go behind head, and the other where the head is dependent and the hands go in front of the face?
For your particular issue I think you need to pick the least painful approach for your artwork, is it for live streaming where some of the tricks won’t work, etc. But hopefully this gives you a few ideas (and hopefully has not made it even more confusing rather than helping!!!)