I am doubtful also that the music would fall under fair use, but I read a few articles on fanvids as fair use and thought it was worth a shot. I can certainly see how the clips from a movie or a TV show are repurposed, but the music is being used fully and straightforwardly. I wish that, for example, OTW addressed the use of copyrighted music on their page about fanvids. The fanvids that they use as an example for how footage falls under fair use have songs that are not under creative commons.

I will probably just go with vimeo, as suggested above.