Officially confirmed to be impossible.
Answer from GitHub support:
Thanks for reaching out to GitHub Support about using GitHub Pages
We set the following Cache-Control header for all GitHub Pages content:
This header is the same for all assets on all sites on our Pages service, and we don't currently provide a way to alter the ...
The server at github.io certainly does caching.
I have a demo up an running over there and was able to determine that the server sets Last-Modified which allows a client to use If-Modified-Since and get 304 from the server if the data has not been modified since it was last fetched. The server also sets CacheControl: max-age=600. I'm not cache specialist ...
It's a bug that YouTube needs to fix. As the player is Flash, there's no possible workaround for this issue. But there's a better way to watch YouTube videos from a PC video player called VLC, if you don't have VLC, search the web for download links.
Open VLC Player -> Click the Media tab in the menu bar -> Select Open Network Stream and paste the video to ...
On an absolute lark, I tried out their new Outlook.com (from the "Options" menu), and the memory usage seems to have dropped from 250M down to 143M.
I'm not sure if the newer site uses a different framework or if they are doing something differently with the message caching, but this seems like a good solution for the time being.