Even if the event is run last, The "problem" with having running scores is that, teams already know who is getting medals before the ceremony even begins.An ultimate event with 5 people from each team in which questions from ALL the events can be asked. It would be run after all the other events, and spectators would be allowed. All teams will participate at the same time and scores would be broadcasted after each question. I'm not explaining it well, but I know they had something like this in the A Div. science olympiad.
Questions will be displayed on a projector, using signalling devices; teams will have 20 seconds to converse and enter in their answers. For each correct answer they will earn points for each incorrect answer they will lose points.