The uv2uv program does exactly what I need, and this user found its website delightful, with the frame and the program logo that looks like it might have been made in Amorphium or something.  Really lovely.  This saved me, potentially, hours of repainting hair textures.  All I had to do was pull the resulting textures into Modo, so I could expand the UV seams.

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Cage can be an opinionated jerk who posts without thinking.  He apologizes for this.  He's honestly not trying to be a turkeyhead.

Cage had some freebies, compatible with Poser 11 and below.  His Python scripts were saved at archive.org, along with the rest of the Morphography site, where they were hosted.