Looking at the UVs is an interesting idea. But I'm just a bit confused now. Are we talking deriving UV mappings from Cage's vertex correspondences, or deriving correspondences from already matching UV mappings for a pair of figures? And why are seams so problematic? I understand that they're a bit tricky, but unless one wanted to match completely unrelated, existing UV mappings - which I don't think would be very useful, anyway - I can't see the big unsolvable problem.

So, what am I missing?

-- I'm not mad at you, just Westphalian.