Anyway, I found this process to be too complicated (especially if you're making lots of small changes in a short time) so I built crxify: a web app which packs your code from GitHub into a .crx-file. Below is a video describing the process.
- find the zipball URL for your repository and the branch / tag to be packed
- the URL usually looks something like this: https://github.com/USER/REPOSITORY/zipball/BRANCHorTAG
- for example: https://github.com/TomTasche/Announcify.js/zipball/0.2 or https://github.com/TomTasche/Announcify.js/zipball/experimental
I hope this provides some real world value for someone. :) Let me know if you need more features!