What is causing softwareupdated to use excessive resources and kill the responsiveness of my Mac?
If you open the Console application I believe it defaults to "All Messages" which might not provide any useful information.

However if you open the Console application, then open the "/var/log" option at the bottom of the left-hand source pane you should find an entry for "install.log". If you select that you should see some information on what softwareupdated is actually doing, or trying to do, to your machine.