Play everyone twice outside the division and six or seven times in the division. Six cuts the schedule to 78 and seven ups it to 83. Both are doable. Of course the league doesn't mess with the playoff format like this.
Whenever you have an odd number of games you lose the fairness of each team having an even number of home games.
I had a similar idea, but still with 6 divisions of 5 teams, but no conferences. To do the schedule, I thought of two different formats.
6 games vs Divisional opponents = 24 games
2 games vs every one else = 50
Play Offs: Top 16, reseed each round
For a shortened season of 74 games every one loses 4 home and 4 road games.
Pros: way less travel, non divisional travel more equal for everyone. With 8 fewer games the schedule can be spread out, leading to fewer back to backs, and hopefully fewer injuries due to wear and tear.
Cons: Weak divisions can lead to unbalanced playoff seedings. Fewer games mean less gate money.
4 games vs Divisional opponents = 16 games
4 games vs two other rotating divisions = 40
2 games vs the remaining three divisions = 30
Play Offs: Top 16, reseed each round
For a longer season of 86 games every one gains 2 home and 2 road games.
Rotating Divisions: Either a set rotation of divisions so that all 5 other divisions will have the expanded schedule twice in a 10yr period
Pros: Fairer travel, more gate revenue, still get to see non divisional opponents more often, weak divisions not as much of an issue.
Cons: More wear and tear can lead to more injuries
Or a strength of Division rotation where the stronger divisions play each other and the weaker play each other based on the previous years point totals.
Pros: More Parity in the league and fairer travel, more gate revenue, get to see non-divisional opponents more often.
Cons: More wear and tear can lead to more injuries
And hear is how I would shape the Divisions and why.
The North (or whatever) Division
Montreal
Ottawa
Toronto
Detroit
Chicago (or Quebec City if say Phoenix were to move)
This gets Detroit mostly eastern TZ opponents, if 4 Canadian teams that's the price for all eastern TZ.
The Atlantic Division
Boston
New York Rangers
New York Islanders
New Jersey
Buffalo
This gets you the Boston/New York rivalry, the cross town rivalry, the cross state rivalry, and the Jersey New york rivalry.
The Eastern Division
Philadelphia
Pittsburgh
Columbus
Washington
Carolina
This is all about giving Columbus a shot, hating Pittsburgh is just natural in Ohio. The cross state rivalry is preserved and who wouldn't want to see Ovechkin and Crosby go head to head every year.
The South Eastern Division
Florida
Tampa Bay
Nashville
St Louis
Dallas
Not an ideal solution for Dallas, but better then the Pacific travel wise. Would love to have a Division with Dallas, St Louis, Chicago, Nashville and Minnesota, but doesn't really work out. Nashville, St Louis, Dallas should make for some good rivalries, and retains the cross state rivalries in Florida.
The Central Division
Edmonton
Calgary
Winnipeg
Minnesota
Colorado (unless Phoenix to QC, then Chicago, if KC then KC)
Pretty much the north west division with Vancouver swapped for Winnipeg.
The Pacific Division
Vancouver
San Jose
LA
Anaheim
Phoenix (Unless they Move, Then Colorado, Maybe Calgary to sweeten the pot for Vancouver)
Really can't get much further west then Vancouver, but a really hard sell to get them to move.