Adding a player or two wont fix this, its a team mental problem and what needs to happen is a changing of the mindset. I remember Lupul was interviewed on TSN last year during a game intermission and they asked him something about being outshot and he replied "We don't care how many shots we give up, as long as its from the outside". That right there is the problem the Leafs are content at playing a passive style and hoping they're goalie holds them in it, it doesn't matter if you keep the teams to the outside because if you keep letting them shoot eventually an outside or point shot is going to trickle in at somepoint. The Leafs need to apply an aggressive mentality in all zones, instead of collapsing back in front of their goalie and giving the other team time/space to set up they should be challenging the points and forcing them into making a bad pass or turnover, if they can do that they'll limit the time spend in their own end. In the offensive end they need to stop with this BS of dumping it in, because its NOT working instead they need to use their speed to back the defense off opening up time/space for quality shots, if they do that then they spend more time in the other teams end and get more shots and a better chance of scoring goals.
This boils down to Randy becoming more open minded and willing to change his stratgey and the players being opened enough to buy into it as a team.