The fix turned out to be properly setting the zimbraAdminPort; I dunno what happened to that in the first place.
Code:
[16:39 root@avocado ~] # su - zimbra
[zimbra@avocado ~]$ zmprov gs `zmhostname` | grep zimbraAdminPort
zimbraAdminPort: 7443
[zimbra@avocado ~]$ zmprov ms `zmhostname` zimbraAdminPort 7071
[zimbra@avocado ~]$ zmprov gs `zmhostname` | grep zimbraAdminPort
zimbraAdminPort: 7071
[zimbra@avocado ~]$