I'm not sure what your reason is to completely shut down Zimbra on the mirror server, but why not try it with Zimbra running on the mirror server? Can't you just disable the same-IP interface on the mirror server, or disconnect it? Will that mess up the redolog or LDAP syncing? The log for the sync should be /opt/zimbra/log/live_sync.log. What does it say?
To replay redo logs only requires that the mailbox process is stopped. This is done automatically by the script. The script will work whether Zimbra has been started on the mirror or not as it will enable or disable services as and when it needs them. Keeping the rest of Zimbra running will drastically reduce the time it takes to fail over. This is only an advantage when access to the server domain can be quickly flipped or has a failover mechanism.