I've written a small demo of a Chrome extension that converts your emails to PDF, and creates a new draft with the PDF in attachment. It uses the chrome.identity api to retrieve the OAuth token.
It is an alpha version, with a lot of bugs. I need to improve the reading of the mails and the parsing of the gmail URL, as well as the global look. But it is still satisfying.
Here's a video of the extension in action.
And here's the github repo with the source code : https://github.com/dhatanian/demo-gmail-api