Unfortunately, there doesn't seem to be a way around the fact that web apps have no persistent access to the local filesystem, and thus would have to duplicate any locally stored music in browser-based storage in order to maintain its own fully synchronized library.
I can understand why this restriction is in place as a security measure, but it significantly limits the appeal of any web app that performs any kind of synchronization of files. I sometimes wonder if persistent filesystem access is really such a huge security risk for web apps that even asking for explicit permission grants from the user and limiting access to user-specified directories is not enough to make it an acceptably secure capability for inclusion in web browsers?