Looooong post because I have come up with the solution to jump (almost) straight into playoffs without having to base the standings on points percentage. If we hit a point where you can only play a full playoffs by skipping the remaining regular season, there is going to be hand wringing about the differences in games played. Teams out of the hunt (or trailing division seeds) with fewer games played will argue that you have to use points percentage. Teams with more points but more games played will argue that actually banking points is more reliable than points percentage. This analysis/proposal gets all teams who are currently within "games in hand striking distance" from each other onto the same number of games played, so the NHL could use pure points without punishing teams with fewer GP.
The Caps/Flyers/Pens have all played 69 games and no one else in the metro can catch them by the 69 game mark. Metro 1-3 can be seeded where they are.
Same with Boston/Tampa/Toronto. 70 games played and Florida can't catch up with their game in hand. Atlantic 1-3 can be seeded where they are.
The Wild card in the East is trickier. Carolina at WC1 has 81 point in 68 games. Columbus has 81 points in 70 games and the Isles have 80 points in 68 games. No one else could hit 81 points in 70 games. Solution: Carolina and the Isles play a 2 game home-and-home. That puts all 3 teams at 70 games played, top 2 teams earn playoff spots.
So you can fairly seed the East with 2 total games played. The West is harder. 1-3 in each division isn't locked in and Vancouver could climb from out of a spot to either a wild card spot or the 3rd spot in the Pacific Division. Also, For Nashville to be on an even GP pace w/ Winnipeg for a Wild Card spot, they could theoretically catch Dallas. Here are the standings of relevant teams for reference since this is complicated:
Defending Stanley Cup Champion St. Louis Blues: 94 points in 71 games played.
Avs: 92 points in 70 games
Dallas: 82 points in 69 games
Vegas: 86 points in 71 games
Edmonton 83 points in 71 games
Calgary: 79 points in 70 games
Winnipeg: 80 points in 71 games
Nashville: 78 points in 69 games
Vancouver: 78 in 69 games
Minnesota: 77 points in 69 games
We need to get everyone to 71 games played.
St. Louis, Vegas, Edmonton, and Winnipeg have already played 71 games. They don't play any games.
Colorado needs to play 1 game
Dallas needs to play 2 games.
Nashville needs to play 2 games.
Vancouver needs to play 2 games.
Minnesota needs to play 2 games
Calgary needs to play 1 game.
That's 5 total games that need to get played to get all the relevant teams in the West to the same number of games played. We can debate the best way to determine who plays who, but I think just random selection is the way to go.
So there you go. 7 total games played league wide and every single team with the potential to alter their playoff seed will end up with the same number of games played as the teams they are competing with. And since no team has to play more than 2 games, you could get this done in 3 nights without anyone having to play a back to back.
If we get to a point where there is just no way to play a good number of regular season games and a full playoffs, I'm fine if the league just says "we're switching to points percentage to determine who makes the playoffs." But if that causes too much whining, this would be the quickest way to let the NHL seed playoffs by pure points instead of points percentage. Every team in the league who hasn't been mathematically eliminated opens a mini-camp on "day 1." These games take place on days 5 and day 7, you can be playing playoff hockey by day 9. Condense the mini camp a day and remove a day of rest and you are down to exactly one week between "safe to play" and "start of playoffs."