The consensus I'm hearing is that the players and league don't want to jump right into playoffs due to injury concerns. Even though a little 1-2 and 3-6 play in tournament isn't the traditional "playoffs" that the NHL usually has, it is still the same intensity (and arguably more intense since there is less margin for error in a 3 game series than a 7 game series). I don't think jumping right into those mini-series addresses the players' concern that they need some tune up games before jumping into playoff intensity.
If that is a deal breaker for the players (which I think it probably is), then it is going to be interesting to see how the NHL structures things. Is the NHL willing to have a week of tune-up games between non-division opponents in these neutral locations and then move some teams once for division playoffs? I think that is a better option than telling teams to go play tune up games vs teams that they will shortly be playing in the playoffs.
For example:
City 1 starts with the top 3 from the Central and 4-6 from the Atlantic: Blues, Avs, Stars, Panthers, Habs, Sabres
City 2 starts with the top 3 from the Atlantic and 4-6 of the Central: Bruins, Lightning, Leafs, Jets, Predators, Wild
City 3 starts with the top 3 from the Metro and 4-6 of the Pacific: Caps, Flyers, Pens, Canucks, Coyotes, Ducks
City 4 starts with the top 3 from the Pacific and 4-6 of the Metro: Golden Knights, Oilers, Flames, Hurricanes, Blue Jackets, Islanders
We don't need to include the bottom 7 teams in the league. Tough break for the still-technically-alive Rangers and Hawks, but let's be honest about their chances. If the NHL really wants these markets to participate, put Chicago in the Pacific instead of the Ducks and put the Rangers in the Atlantic instead of the Sabres. Either way, I'm fine saying we only need to include 24 teams in this thing.
Each team plays the 3 teams from the opposite Conference in games that don't count towards the standings at all. These are essentially pre-season games against teams that you are least likely to see in the playoffs in order to minimize the incentive for cheap shots. That gives you 3 tune-up games that can be completed in a week with the lowest injury chance possible. If teams/players want 6 games, you play each opposite Conference team twice.
Then you move half the teams so that you get everyone from each division in the same city. The top 3 teams get to stay in the same place as a minor reward for being in the top half of the division. With the way I structured it, it minimizes the cross contamination as much as possible. Cities 1 and 2 are swapping teams and so are cities 3 and 4. Cities 1 and 2 don't receive anyone from cities 3 and 4 and vice versa.
City 1 now has the 6 Central teams: Blues, Avs, Stars, Jets, Preds, Wild
City 2 now has the 6 Atlantic teams: Bruins, Lightning, Leafs, Panthers, Habs, Sabres
City 3 now has the 6 Metro teams: Caps, Flyers, Pens, Hurricans, Jackets, Islanders
City 4 now has the 6 Pacific teams: Knights, Oilers, Flames, Canucks, Coyotes, Ducks
Now you start the 1 vs 2 mini-series for seeding plus the 3 vs 6 and 4 vs 5 mini series to determine who makes the playoffs. Once you have the 4 playoff teams from each division, you leave those 4 teams in the same city and do an all division rounds 1 and 2.