We've started using a private Gitlab installation for project management (Git, Bug-tracking and so on). I know it's fairly trivial to share out or mirror the Git repos, but what about the Issue Tracking content?
I see Gitlab offers a fairly involved and tedious method to manually back up and restore a Gitlab installation, but I'm looking for close to real time mirroring in case of hard drive failure or other catastrophes..
Git repositories can be easily mirrored using Git protocol. Other types of data in GitLab are stored in the database and can't be mirrored in the same way.
Using a good old backup and restore process is probably the best solution for the situation you described. GitLab has this documented at https://docs.gitlab.com/ee/raketasks/backup_restore.html. The process really isn't that difficult - gitlab-rake gitlab:backup:create to create a backup, and gitlab-rake gitlab:backup:restore BACKUP=<timestamp> to restore.
If you need a higher level of service, GitLab supports high availability - https://docs.gitlab.com/ee/administration/high_availability/