Another interesting twist might be something similar to relegation.
The 13 non-playoff teams get put into a pool each season.
The 13 worst playoff teams (by record) get to "draft" these teams into their divisions, with the stipulation that we still have divisions of 7 teams and one division with 8 teams.
So, for instance, the Celtics would have gotten first pick of a team from the non-playoff teams to pull into their division. Maybe they want to steal the Cavs from the Central. Then the Pistons pick. They want the Knicks from the Atlantic. The 76ers pick next; they pull the Nuggets into the Atlantic, etc.
Also means once you miss the playoffs, you don't know what division you'll end up in next season. Another nice little incentive to make the playoffs.
Just a thought.