Browser back button works fine in chrome on a Android with amp pages fwiw. Does safari mobile not support the session history management APIs? caniuse says it does, but it sounds like it doesn't work from what you're saying.
[0] https://developer.mozilla.org/en-US/docs/Web/API/History_API...
https://www.w3.org/TR/encrypted-media/
edit: I can see it. Next iteration you will need a AMP key to publish your content and clients will need AMP key to consume content! Browsers that don't include the key will be excluded from the ampweb.
https://www.usatoday.com/story/money/cars/2015/06/29/america...
Soso link, but makes my point.