I'm surprised no one else has brought up Oxide's process, which has a similar writing-heavy stage as part of the application. See https://docs.google.com/document/d/1Xtofg-fMQfZoq8Y3oSAKjEgD... for what they ask for.
It's not quite as much as Canonical, but it's still a _lot_ of writing to go through just to apply for a position. I considered applying there during my last job search but I just wasn't enthused about it enough to spend all that time writing before I even knew if they had any interest in me.