Thanks, Angelo.
I know how to exclude categories; what I would like is to exclude by id instead or otherwise exclude the ‘active’ event being displayed by single-event.php.
After more digging, it looks like for a multisite installation that all of the event category management has to be done through the network hub. By going there, I am able to manage the event categories normally. All of the sites on the network have to share categories (which is OK for me in this instance).
This may be a result of my settings; I’m not sure. Just posting in case anyone else has this problem.