We can have a 12-team World Cup instead of an All-Star break. 3 groups, 4 teams in each, round-robin. Best two teams from each group advance to quarterfinals, so do two best third-place teams. Then, quarterfinals, semifinals, final (and maybe a third-place game). Six games max for each team, two weeks should be more than enough.
Nine best teams (top three in each group) keep their World Cup spots for next year, the last-place teams don't. These three spots are determined in... the World Championship! Three best teams in the World Championship (not counting the nine automatic qualifiers) will go to the next year's World Cup. That will surely make the World Championship more interesting, even without most Stanley Cup players.
And the Olympics? Who cares, really? Just like no one really cares about the soccer tournament in the Summer Olympics...