A key element of my idea was that it involved everyone in the playoffs. While this might seem to make the regular season meaningless, I think it could actually make the regular season more meaningful.
The bottom 4 teams in each conference would face the bottom 4 teams in the opposite conference, but they would carry their regular season records against the other 7 teams into this classification group. The classification of teams 9th to 16th would be based on 14 games, 10 during the regular season, plus 4 more in the playoffs. Four teams (13th through 16th) would relegate directly just like now. The 11th and 12th place teams would have to defend their place in the upper division, while the 9th and 10th place teams would have to defend their place. The 9th and 10th place teams would retain their place in the upper division.
The top 4 teams (the two conference winners, plus the two other teams with the best record) would compete for the league championship and direct promotion. This would mean that the regular season record was more meaningful, since only 4 teams would have a chance for direct promotion. It would also permit best of 3-series for both rounds. The 3 teams that lose in the championship playoffs would get a 2nd chance to promote.
The next 4 teams (5th through 8th) would be competing for the chance to challenge a team from the upper division. If we have 4 leagues, there would be 16 teams involved. They would be placed in 4-team inter-league groups, and play 3 games, so that 4 teams would advance. They would be joined by the 4 winners of games between losers of the champions semifinals, for a total of 8 teams.
These teams would play another two knockout rounds, resulting in two teams remaining. They would be joined by the 4 championship finals losers, and the 11th and 12th place teams from the division above (8 teams). Two more knockout rounds would determine the 2 teams that would compete in the upper division the following season.
All teams would have at least 3 playoff games, and be involved for most of the two weeks of the playoffs, with a Saturday arranged scrimmage for those teams (20 of 64) that were eliminated before then.
The final week would be the interdivisional playoff. Since only 14 of 64 teams would be involved, the other 50 teams could have an off date on Tuesday, which gives some sense of an off-season.