I found a solution using collada export, this exports an unbroken mesh and animation. I have to export morphs separately one by one, which is a pain, but at least I have found a way out of Poser for weightmapped characters.

The other problem with collada is that conformers do not export correctly.

Maybe one day SM will fix some of their exporters, in fact, I consider their leaving the obj export in such a useless state as inexcusable.