I'm not sure I like the approach of serving files from your repository. I'm not sure about how git works in detail, but are repository updates even atomic?

When I deploy my website, I use a different approach: My webroot is just a symlink. My deployment script exports the repository to a directory with a unique name for every commit. When the export succeeds, the symlink is updated to point to the new directory.

The advantage: Changing to the new version is instantaneous. If something should go wrong, I can immediately revert by changing the symlink back to the old dir.