After some juggling between Poser, Blender and the Unix sed program, I now have an OBJ with the new mesh and the correct grouping. So in particular, the eyes can now move about without exploding. I've also had a closer look at the JCMs and it seems that they're only a bit off at the body part seams. Should be an easy fix.

-- I'm not mad at you, just Westphalian.