Hey @brianjking. Sorry for my absence of belief, I was almost giving it up.
Thank you so much for guiding me in the right direction!
HTTP/2 indeed works without --nginxmainline on latest EE.
Now https://tools.keycdn.com/http2-test validates it just as expected!
All the other stuff regarding the HTTP/2 activation was just fine, no issues. It turns out when reloading nginx I've came through a warning related to a duplicate server location directive, so nginx wouldn't restart and I was actually hitting an old version of my website's cache in the browser.
I'm so glad it works. Thanks for your time!