I'm actually not saying this because it would help the Leafs chances but because I think it'd make the game better and teams going for it more.
My proposal would be cut the OT loss point and cut the shootout. After that I don't know yet. Sudden death OT in November doesn't sound very appealing but you can change the rules of OT enough to increase the likelihood of a winning goal and have them play until that happens.
4 on 4 for a minute to 3 on 3 for a minute to 2 on 2 for 3 minutes or whatever. Shootouts are boring as shit and irrelevant as you mentioned. Someone can figure out a better way. NFL, NBA, MLB all have a winner or a loser at the end of the game.
The NHL used to do this not too long ago. Then fans used to complain that teams got nothing for tying a game and then only losing in the five minute overtime. It is much better now that teams get rewarded for tying a game I think by far. Though I agree with you the shootout should go. I think it is fun as fuck to watch, but it prevents teams from trying to win a game. I doubt the NHL will take away the point for tying system while I can easily see the shootout leaving.