Tom911 is correct. United's CTO is level 5, 10 Barrack Street. In city centre, near GPO and main Wynyard train station. They may be able to assist as the ticket is on their paper.
I am surprised 'Orbitz' is not required to retain and work within the same legal connection times the airlines use? What if they said it was 50 minutes. Or 26 minutes? Surely they are required to ticket using legal connection times? And if not, allow a change to ensure they do. Once again, there is no way known if both flights are on time that one hour will work for you.
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~ Glen ~