Hi there, thanks for making this! This may be way too complicated to implement, but I thought I'd suggest it just in case it's easier than I think it might be. If you want to have something displayed that you need to log into securely, then it's probably easier to, instead of retrieving what's at a URI in this app, send the URI to a browser app, one in which you're already signed in to that site, and take a screenshot of the result.
As an example, you could set the URI to be calendar.google.com and the browser app to be Opera Mini. Then this app would load that URI in Opera Mini, screencap the result (your google calendar) and set that to be the screensaver.