I've occasionally suggested that they should try making the shootout a pre-game thing.
Winner of the SO wins if the game ends in a tie, just like now. Only difference is, since you know who that is, the team that's behind (or tied but without the SO win advantage) needs to get it done before regulation time is over.
You could remove the OT, and since every game starts with a SO, they all last more or less the same. (Unless the SO runs long.)
Never going to happen obviously