Yes you can on iOS7: http://stackoverflow.com/questions/19664206/access-the-javas...

I know, but that isn't a realistic option since it's not a public API and therefore not something you should use in a production application.

Yes, this is a private api - meaning not officially public so can't use it in production. I would love to have the new FTL JIT engine supported officially for the webview JS execution. It would bring UIWebView on iOS7 up to par with Android WebView on Android 4.4