To elaborate on the loser's bracket idea, this is what it could look like:
Division semifinals
Same thing as what is currently being done.
Division finals
2nd round of the regular playoffs go on as planned.
Losers of the first round of the playoffs from both divisions of the same conference go up against the consolation round winners. This would mean there are now six teams in the loser's bracket in each conference. Matchups could be 1v6, 2v5, 3v4, meaning that intra division play is on display now. Matchups could be determined by the amount of votes that each team received in the regular season, regardless of division difference.
Conference finals
3rd round of the regular playoffs go on as planned.
Three teams should be left over from the loser's bracket, with two new teams joining the bracket, bringing the total to five. This isn't ideal as five isn't an even number. My suggestion is to give the team with the highest regular amount of regular season votes a bye (explained later), thus the matchups would be 2v5, and 3v4, with the same seeding system as I proposed above.
3a round:
The winners of the 2v5 and 3v4 matchups mentioned above face off, and the winner gets to face off against the team that got the bye.
Playoff finals
The two best teams from each conference that advanced through the regular playoffs bracket face off against each other.
The winner of the 3a round in the loser's bracket faces off against the loser of the conference finals.
4a round:
The ATD final is put on hold as the winner of the loser's bracket from the previous round goes up against the playoff finals loser.
ATD Final:
The winner of the playoff finals goes up against the loser's bracket champion for the ATD crown.
Pros:
-Consolation winners get a shot at the big prize, giving them more incentive.
-Playoff losers have a second chance, minimizing the damage of being put in so called "divisions of death".
-Everyone gets to participate a bit longer (except for the losers of the consolation matchup in the 1st round)
-The longer someone is actively involved, the higher the chance that they'll vote on playoff results down the line.
Cons:
-More work for the administrative team.
-ATD takes longer to finish due to the presence of two extra rounds (3a and 4a).
-ATD Finals could be the same matchup as the playoff finals.
-Kind of defeats the purpose of hiding seedings
-TLDR.