If you can break same origin policy submit a bug to Google. That would be a significant defect that would warrant their top tier bug bounty.
Seriously, use HTTPS for everything. Not to be rude at all (seriously!), but it’s pretty obvious by this thread and the other you linked to that you don’t have the knowledge/experience on this topic, so do your users a favor and trust when I say you need to be using HTTPS.
[0] https://www.theregister.co.uk/2015/03/27/github_under_fire_f...
SOP offers zero protection against this. Just load evil.com?data=XYZ in an iframe.
Where? I’m happy to prove the attack vector if necessary, would be trivial for me to do if the app is designed the way you described it (and no, not eligible for any Google bounty as this has nothing to do with same origin policy).
If someone man-in-the-middled the downloading of the app code (trivial, if not HTTPS), then none of those constraints you later mention would be true and the user’s data is now compromised.