For anyone else that searches this topic, the easiest way to migrate your ZD to a new IP (assuming your AP subnet is routed) is to use the Limited ZD Discovery.
Set your current ZD IP as the Primary and the new ZD IP as the secondary.
Give it a few mins for the changes to replicate to the APs, then change the IP of your ZD to the new IP and wait for the APs to connection.
Once they're all connected, go in and clean up the Limited ZD Discovery.