John Marchesini answered my question as follows:
If you navigate to ‘Enterprise > Update Services’ in the left side of the console, you should see a list of your WSUS servers appear in the top center pane. Select the server you want to nuke, and in the bottom right pane in the console, there is a ‘Delete’ action which will blow away the server, its inventory data (if any), and it’s management group affiliation.
You can then use the ‘Update Server Registration Management’ action on the right side of the console to add the new server. Don’t forget that you will need to add this new server to a management group via the Management Group Wizard.