Mischief managed. Just POST the message to https://www.googleapis.com/upload/gmail/v1/users/me/messages/send?uploadType=media with these headers...
Authorization: Bearer <access token>
Content-Type: message/rfc822
Content-Length: <message size>
... and you're good to go.
On second thought, Google appears to feel free to clobber message headers if you do this. (For example, "format=flowed" disappears.) Going back to mutt's built-in smtp transport instead.
@david I've just started using Mutt again, too. Also with Gmail at work. Very exciting indeed.
Now to figure out how to send... I usually use msmtp, but I know I've got some python code to send email using Google's API lying around somewhere.