I like the ideas for seeding the teams. It might be enough to seed 2 or 3 teams per division according to the previous seasons performance, and then seed everyone else randomly.
I don't think it would lessen the importance of regular season wins, as you would still need to win many matches to end up within the first 4 teams in your division, specially as you would face at least 2 potentially strong teams in each division.
Would we have done this in the current season, then the teams ranked 11^th and 15^th would have dropped to the best of the rest playoffs (2 teams only). Those teams had teams ranked 1, 7, 9 and 2, 3, 4 in their division, with a more balanced division seeding this might even not have happened.

This is the proposal for balanced divisions in one post, considering the different feedback given.
Regular Season

1. Seed the first 4 teams of the previous season into the 4 divisions
2. Seed the next 4 teams into the 4 divisions
3. Seed the next 8 teams into the 4 divisions
4. Seed all remaining teams into the 4 divisions

Scheduling is done as usual, each team plays each team in the division once during the season, for other matches adversaries are randomly chosen, each team plays equal number of home and away matches.
Playoffs

1. The first 2 rounds of the Championship playoffs are played within the division, e.g. solids1-solids4, solids2-solids3, then the winner of both determine the division playoff winner.
2. The last 2 rounds are played for the league Championship, e.g. winner of solids vs stripes, winner of high vs low ball division.
3. The best of the rest bracket plays the playoffs following the bracket ranking, which is the same as it was done during the past few seasons.

Merits

1. More importance given to division ranking during the season.
2. The random seeding of teams for the regular season is maintained, but there is a better balance of playing stronger and weaker teams during the season.
3. Rankings, statistics, and player history will be consistent with past seasons.

Yes, that would be the proposal.