Once you have backup copy of /opt/zimbra (or built-in hot backups with ne), anything 5.0.2 or above can upgrade directly to 6.0.7.1
I think we've since eliminited most of the problem, but if going to a lower version make sure your commercial or self-signed certificates are valid/not expired first.
The available upgrade paths: 4.5.0 - 4.5.6 > 4.5.11 > (
LDAP replica step) > 5.0.2 - 5.0.23 > 6.0.0 - 6.0.7