You can do this in Terminal.app without a ton of pain.
Stop Plex.
Do this to get a list of what’s in there:
% defaults read com.plexapp.plexmediaserver
Then do this to remove the ...Identifier
keys and the old token.
% defaults delete com.plexapp.plexmediaserver AnonymousMachineIdentifier
% defaults delete com.plexapp.plexmediaserver CertificateUUID
% defaults delete com.plexapp.plexmediaserver MachineIdentifier
% defaults delete com.plexapp.plexmediaserver ProcessedMachineIdentifier
% defaults delete com.plexapp.plexmediaserver PlexOnlineToken