I think it is insane to do this as a grouping game.
I would just spread those five letters around in a circle and draw a line between two letters if they're connected. That's not to say the other way won't work, but double-recording a connection in each dude's column is too much mental labor for me.
I'd rather just use an atypical diagram that better matches the story we have to track.
The game is definitely annoying and involves lots of plug and chug, so switching to the simpler diagram isn't a game-changer. It just means, as you said, that we spend less time up front and get to work on drawing out lots of little hypotheticals.