If you're willing to get your hands dirty, you could probably set up an hourly cron job that will periodically do a git pull/fetch for a given (or several of the) repo's.
Hell, you could write a script in SB to do it, and just schedule it with cron. The alternative would be a Bash/Python/Ruby script, or some compiled binary.
All you would need to do in the script is CD into the repo root, and issue the appropriate git command.
This is all theoretical, I'm not sure if GitLab does something funky with the repo's.
A good way to test is to use a repo you control on, say, GitHub and mirror it in GitLab. Then set up what I've suggested above. Then make a change in the GitHub repo, and see if the change is reflected in GitLab (after the update period you set up in the cron job, of course).
Unlike modifying the GitLab code, this shouldn't violate their TOS since a git repo is a git repo in the end....they just make it simple for the terminal-challenged.
AIR.