@UuQui3ai I just wrote a plugin for uploading tracks from beets to iBroadcast:
And there are iBroadcast mobile apps which support locally caching the media files. Not sure if that would meet your needs—it would only be one way.
Another more hacker-ish solution I was looking at is Astiga, which is open source and might let you achieve what you want with some development effort?
From a more sync-centric perspective: I’ve been playing with Syncthing which seems pretty awesome, supports bidirectional sync, and also has an Android app. But unfortunately no iOS/iPhone app.