+1 to reusing the IPs as an easy option. If you backup and restore all of the configuration to the new appliance, it will have a record of all of the agents and be able to "take over" seamlessly.
If they are connected by hostname, you could just update the DNS entry and everything will work.
There is a command on the appliance you can run BEFORE you disconnect all of your agents to tell them to connect to a new system (IP or hostname); they'll disconnect and reconnect to the new appliance. The catch is you have to do it before you disconnect anything, and any offline agents won't get the update.
If none of those sound good, you'll have to edit your agents' configuration files/clear certificates and reconnect them all (maybe a GPO).