I imagine if they stripped off all the stuff from their own sites that doesn't show up on AMP the speed would basically be the same, and they wouldn't be under Google's thumb.
No massive header with lots of images of other stories, no master folder with lots of images of other stories, no giant sidebar with lots of images of other stories… get rid of all of them. All of a sudden your page is really fast and doesn't take 45s to load.
Remember what the web was like on dial-up? Design pages for that but with large images. Text goes a LONG way for navigation and discovery of other stories. You don't need ridiculous big images.
Do something really simple. Make a page with content that looks exactly like the AMP page. AB test that against the AMP page. I'd be willing to bet they basically perform the same, modulo any benefit Google gives you for being part of their lock-in.
Text articles with pictures do not require the complexity of googles infrastructure and systems to be fast and lite.