So, it absolutely must be PSB, not PSD, despite the tool being called "PSD importer". PSB is just PSD for images over 2GB, but, unfortunately, free tools like The GIMP can't write this format. However, I found that simply renaming a PSD to PSB will trick this importer tool into importing a PSD correctly.

If you're not getting the "character rig" option at all it MUST be PSB! Rename it if you have to.