I enjoy using Mailbox to the point that I rarely use desktop Gmail anymore -- a keyboard on my iPad helps. It's also easy enough to implement the filtered inbox views mentioned in the article for Mailbox folders, allowing the same sorting functionality on mobile (unlike the star-based solution).
Classic. I just finished a rotation-based training program, and this is how my co-workers and I got through the constant travel. The TSA never took any issue with it, and many folks were quite amused/inspired by it.