Quote - I'm going to have to tear the %*%@#!! geometry up and bring it back into Poser in separate pieces, right?

I suspect you are barking up the wrong tree, thinking about the geometry. My guess is that this is a shader problem.

Quote - If I remove the trans map and make the whole thing transparent, the problem disappears.

That sounds a lot like the classic Transparency_Falloff is not zero or black parts of mask are not true black problem, as mentioned by Miss Nancy.

Have you checked these things:

Transparency set to 1.
Transparency_Edge set to 0.
Transparency_Falloff set to 0.

Use a colour picker to check that the fully transparent parts of the mask are pure black, #000000.

Plugging the mask into the Specular_Value, should prevent you getting specular highlights on the transparent parts.

If you show us a screen shot from your material room, it may provide some clue.