I don’t know the gitlab authentication pieces very well, but isn’t there a password-based authentication alongside the LDAP auth? If LDAP goes down, I suspect there is still an admin login that can get in to gitlab, no? If that’s the case, why not just create another user using the password-based authentication for this purpose? Can you not use username/password-based authentication either?
Sorry that I’m not being specific. (See my first sentence.) Good luck.