Alpha Matte Multiple Layers while keeping Parent Properties

Let's just start with layer 1 Body Outlines. I see an End keyframe so I am assuming that there some kind of shape animator on that layer like animate position and rotation.

Below on layer 4, I see another shape layer named Body Mask Outlines. I am assuming that this layer has a white fill. I would know a lot more if you selected the Body Mask Outlines layer and pressed the U key twice so there was some indication of what you are doing in the layer.

I might be wrong about how you are rotating the body and moving it up. If parenting is working then you are not using a position and rotation animator, you have animated the position and rotation of the layer. If parenting is working and the move is working and the body mask moves as it should all you have to do is turn off the visibility of the body mask layer and apply Set Matte to all of the layers you want to hide. 

The screenshot helps but I still don't know exactly what you are trying to accomplish. 

If this was my project and I wanted to rotate and move the drawing of the bird in front of the bottom nested Elements comp I would just pre-compose everything that makes the bird outlines to one comp called bird and the everything you want to use as a matte for the bird into a bird matte comp, turn off the bird matte comp and use Set Matte on Elements. The other option is to group all of the mattes in a single pre-comp and use that as a track matte for the elements layer. 

If everything is moving with the same animation then you can tie things together with simple pickwhip expressions even across comps. It's pretty easy to do.

I could give you a better explanation if you gave me more workflow and design ideas. Let me take one more try. As I look at your comp and read your explanation again I think that you have a sword and a bird that move into place the way you want them to and you want them to cover the bottom layer so you don't see the lines in the element layer. I also think that you don't want to just put a black background on the sword and bird images to hide the lines of the bottom layer. If that is the case and you don't want to go through the trouble of using expressions to tie the animation in one comp to the animation in another comp then there is a much easier solution. Just add 4 copies of set matte, Left Wing, Right Wing, Body and sword mask outlines to the Elements layer and then turn off the visibility of all matte layers. All that is left is to invert the matte in every instance of Set Matte so it makes holes in the "elements" layer.