Is there anything stopping you from also syncing an encrypted copy of your data to a central server to be synced down or your other devices? It doesn’t appear so.
A websocket between all your devices and a server (or even webrtc between devices) could achieve this in parallel.
I was going to mention WebRTC! It seems designed for video calling, but there are lots of cool use cases - I recently ran across https://github.com/dmotz/trystero , a dead simple WebRTC library for peer-to-peer multiplayer browser games.
A websocket between all your devices and a server (or even webrtc between devices) could achieve this in parallel.