Phoenix: adriandurden is already on the network edition (as you mentioned in your second post but not in your third?).
Alauppe: Why does it matter if the old server is listening on the LDAP port or not? The backup has the LDAP database in it. Did you read
Moving ZCS to New Server - Zimbra :: Wiki?
Adriandurden: An rsync of /opt/zimbra/backup should be sufficient as long as it doesn't run while the backup is running. As you can imply from the wiki article, this is all you should need (provided you install the exact same version of Zimbra on the server you are restoring to).
To both of you: I could easily be wrong here as I have no NE to test with (yet... building a VM soon), but I would think you should be able to just copy the latest full backup and any incremental backups after that and then try to restore from that. Be careful though as I think I have seen that it runs a "full" backup on user creation that just contains that user. Is there any particular reason you aren't just copying the entire /opt/zimbra/backup directory? If it is too large, why not do a network mount of the folder?