I just flipped through the Character Burner. I didn't see a doppelganger song.
It doesn't mean we can't burn up one... but it seems more akin to Sorcery or some Mannish magic. It's not really an "Elven" thing, in the Tolkienesque context of BW, since Elves are a purer expression of the "song of creation" - why change form when you are perfect?
So, options & ideas.
1) New Elven song. Break the context of Tolkien-style Elves.
2) Ditch the doppelgangers. Use Threne of the Chameleon instead, and say the Tleil'laxu are mostly uber-isolationist, stern Rangers... Borderline Dark Elves.
3) Use Fey-blooded Humans (Half Elves) with the Gift for the Facedancers.