I don’t see a way around drawing the motion paths newly in AE or AI, as they would have to follow very specific routes. But having a 3D object as a reference should make this fairly straightforward.
Another option that comes to mind is animating textures along the surfaces of the sub-objects in 3D. But I seriously doubt that would make it any easier.
Perhaps an expression (or two) that places the layer in a certain 3D position depending on the layer index number? Then you could just import all the pictures copy and paste the expression and they would be placed automatically.
Since there is no perspective change, just a zoom in, you could get away tracking just one point, attaching a screen-shaped mask to it and doing the scaling keyframes manually. People in front of the screen will have to be rotoed.