Vocals: Merril Garbus of tUnE-yArDs, Matt Berninger of The National and Fiona Apple of... herself, I guess. In this hypothetical band, unusual harmonies are going to be key; these three voices are really distinctive in their own way and I think they'd really blend nicely together.
Piano: The aforementioned Fiona Apple. I thought about Regina Spektor in her place, but I honestly prefer Apple's animalistic playing. If I can't have Chopin on account of him being dead and all, I'll have the next best thing!
Violin: Lucia Micarelli of Treme. Yes, the TV show. Every time I hear her play on the show, I get goosebumps. End of.
Guitar: Lindsey Buckingham of Fleetwood Mac. A little bit underrated as a guiatarist in comparison to his songwriting and singing abilities, but most of Fleetwood Mac's best stuff has his guitar chops to thank for it.
Drums: Meg White of The White Stripes. Again, the animalistic nature of her drumming seems to be a great fit with the tribal themes and motif the rest of the band has going on!
Aaaaaaand the rest: The entirety of Los Campesinos! would be session musicians, as those crazy kids can play, like, 30 instruments. When I want a random trombone or flute or whatever, I'll call these guys up to provide! :D