That's something we're definitely considering. One idea that we've been noodling on is to add a downloadable app that managed all your storage and had a simple http rest api. Then in the extension, you could optionally point to that instead of the internal storage mechanism.

That would provide some internal benefits of being able to use a beefier storage backend decoupled from the browser. Users then could run the app locally on their computer, or on their own server somewhere, or potentially as part of a cloud storage service.

A simple workaround might be using dropbox to sync the sqlite db file. It would be nice to have an integrated solution though.