Here is my solution that pleases everybody, the players, the GMs, the league, the sponsors, the television partners.
1) The regular season is officially over. (But hockey isn't over...read on)
2) Standings are conducted via point percentage.
3) Regular lottery, with the bottom 15 teams involved.
4) Because the season is over, teams are allowed to trade players.
5) Replace the Stanley Cup Playoffs with either a 31 team tournament, or a two different tournaments, a tournament with each Canadian team, and larger tournament with the American teams. (or round robin)
6) The tournament will use 20-21 rosters (hence the trading). Teams that were seeded in playoff spots will get some sort of concessions in the form of byes.
7) As far as branding and marketing goes, I haven't thought that far ahead....It won't be for the Stanley Cup. Although, I really do like the idea of a winner of a "Canadian Cup" tournament and an "American Cup" tournament facing in a big Super Bowl type challenge game to crown the Stanley Cup champion. If they do go that route, it won't be recorded as the 19-20 season Stanley Cup Champion, there'll be an asterisk.
(I'm assuming crossing boarders might be an issue, hence tournaments being separated by country. Honestly, a round robin tournament with all Canadian teams would be wild.)
People will say it's not fair that they'd meshing the 2020 season with the 2021 season by using 2021 rosters, but they really aren't. The tournaments would basically be a novelty to appease the networks for lost content and try to recoup as much lost revenue as possible. The only reason the 2020 season even plays into the tournament would be to give some sort of consolation to the teams who weren't given a draft lottery spot.
Basically solves all the problems, assuming the networks and NHLPA would be on board.