Here is my first attempt using this style, which can be viewed here.
Ahem, let me start again to be more clear:
Solution: First, it turns out we can make the gh-pages branch the default. This setting is in the Settings tab, right beneath the repository name changer. Second, it turns out we can remove the master branch entirely from github, so that nobody accidentally checks out that branch, by doing this: git push origin :master. I then delete my local repo and re-clone it.
Update: It is possible to create a gh-pages branch, set it to the default, and delete the master branch, all from the github website :)