layered 2d plane meshes ordering messes up when rotated

I have set up a 2d character with body parts made up of planes with body part textures on them.

The body parts are staggered in their layering in the z-axis so that the correct body parts are seen from the front.

I would like to have the option of rotating in the x or y axes, to give a feel of a 3d flipping to the game, but if I rotate it just a little to much, the ordering of the layers become messed up so that the wrong body part is shown in front, like the back leg peaks out in front or something.

Any way I can fix this? The plane layers are pretty close to each other, but I don't really want to make the layering too spaced apart.