(Edit: another thought, maybe your curl testing took longer with all the extra CSS in the download and writing to disk if that's what you did - an AMP requirement. But did your curling pull down the external CSS/JS for non-AMP?)
According to the webpagetest.org results you linked, which ran the test 9 times on each page, the mean time to first byte for the AMP page is 1005, and for non-AMP it's 989.
Which is just 16 ms.
But the time to visually complete for example on non-AMP is 1955, and on AMP it's 2166.
Which is a difference of 211 ms (which percentage wise is almost 10x bigger (I think, I'm not super mathy)
This implies to me that the problem is AMP not the server.
But if your data is correct then perhaps something is up.
The thing is, I know how the site is coded. The AMP version just excludes things almost exclusively. Although it does have to render the CSS in place (the fragment is cached) rather than just link to a stylesheet.
But here's the thing, even if that is the problem, the only reason it's like that is because that's what AMP requires.
Maybe there's changes we could make on the server, but according to this webpagetest site, the problem doesn't appear to be the server nearly as much as the rest of the render process.