It’s only in the enterprise edition and on GitLab.com, but GitLab has introduced this feature directly, without any workarounds.
They’ve documented pulling/pushing from/to a remote repository in GitLab Docs → User Docs → Projects → Repositories → Mirroring.
It’s in the same section of configuration that you can push, too:
- From within a project use the gear icon to select Mirror Repository
- Scroll down to Push to a remote repository
- Checkmark Remote mirror repository: Automatically update the remote mirror’s branches, tags, and commits from this repository every hour.
- Enter the repository you want to update; for GitHub you can include your username and password in the URL, like so:
https://yourgithubusername:[email protected]/agaric/guts_discuss_resource.git
Note that I haven’t tried it, but you should be able to push to and pull from the same repository. It’s working great for me pulling from a remote repository (drupal.org), and pushing to a different remote repository (gitlab.com).