Ah, probably I understand what you want to create. You want to place moving parts on the surface of a three-dimensional shape like the one shown in this tip, right?:
Spine Tips: 6 cube2
I think the key to achieving what you want to do is to put a bone for fixing in your skeleton. I have created an example, though very rough:
The animation rig above is shown below:
The cube in the tip I introduced first is bound to only two bones, but this time the yellow box is bound to three bones, and the
root bone taking the role of fixation. This creates room to add weights for other bones, and the mouth mesh has additional weights for mouth control there:
In the above example, I animated images that already have perspective, but ideally, the original images should have no perspective. Distorting images on Spine to add perspective would be easier to rig and more beautiful result. The workflow for creating an animation with perspective from non-perspective images is explained in detail on the following page:
I hope this will help you.