Well, that trick with making a thin row of polygons worked out quite well. Thank you, Amacord! But now, I've got a new and very bizarre artifact, as seen in this picture.

It seems that the shadow that would be cast by the front of the shirt onto, well, the inside back of the shirt is instead being cast onto the front of the shirt itself!! All the normals are pointed the right way.

I don't know, I'm stumped. I've never seen this before. Any ideas??