First, I tried to figure out the current options for offline storage in the mobile app.
The alternative standard, IndexedDB, is much less wide-spread, and less performant.
So far, I'm considering using this Ydn-DB library to create an intermediate layer for data persisting.
Native wrapper for HTML5 app
This library allows to create a native app, which wraps a Web-browser and which provides a bunch of APIs for accessing native features of the device.
The first thing which stroke me was that I had to use symbolic links to share common part of the app between iOS and Android versions of the same application.
The code of the application is deployed with the native app, but you can make AJAX calls to remote servers (though I didn't test it yet).
By the way, Android plugin for IntelliJ IDEA works with Android Cordova app just fine :)