Use a likeness to the English soccer system by creating three tiers based on relative competitiveness and financial success.
Now lets be honest; the three tiers would not be equal BUT the opportunity for promotion and demotion is there. Lucrative TV contracts and sold out arenas await teams in the "Premier" league BUT opportunity to win for "have-not" teams awaits in say a second or third. If you still want to have the top eight advance from each league to a playoff format then so be it but the overlaying point is to allow teams of all economic systems the chance to succeed.
Another huge plus to this system would be creating 15 brand new teams in the third division; this allows small financial investment for locales where the NHL would like to be but population, corporations, large enough arena etc do not exist.
This is true parity. You give all teams the opportunity to win a championship that matches the level of commitment by their ownership group. Do the rich get richer...yes. But that is sports; you win...you win.
Here is a sample of the League with the corresponding divisions based on each teams value by 2010 Forbes.
Detroit Red Wings
Los Angeles Kings
New Jersey Devils
New York Rangers
Toronto Maple Leafs
Atlanta Thrashers/Winnipeg Jets
Columbus Blue Jackets
New York Islanders
San Jose Sharks
St. Louis Blues
Tampa Bay Lightning
Third Division (speculative)
The way you ensure parity is you promote the top three promoters in the second and third divisions and demote the bottom three in the premier and second divisions.
It is a different system but one that perhaps could benefit North American sport.