Ok, spoke to support. It looks like RedPhantom's idea was spot on. Support noted there were no facet groups in the .obj file (which would be lines starting with "g") that I sent them. And Poser needs those to assign the geometry to the figure's body parts in the scene.

However when I did some additional looking around (thought I would compare the .cr2 file to see if it had any hints), I found there was another copy of the .obj file by the same name in the Characters folder. So I guess initially it pulled the one from Characters because it was in the same folder as the .cr2 file, but on reloading it went for the one in the Geometries folder, and that's what failed. I copied the one from Characters over the one in the Geometries folder and it worked correctly.