I think you'd use VLC's modular architecture to your advantage. Maybe you'd start with an Emscripten port, but then replace parts with a "native" JS implementation of tracker music support.
That's the first time I've heard of MediaSource being able to play from archives, though - do you have any more info?
MediaSource doesn't specifically support archives; it gives Javascript the more general ability to generate data to be presented by an <audio> or <video> element. How the Javascript code decides to generate that data is up to it -- be it loading chunks over HTTP, pulling them out of an archive, generating them from scratch...
That's the first time I've heard of MediaSource being able to play from archives, though - do you have any more info?