NFL started sucking when they went to four team divisions. They should do it like the SEC. Divide each conference into east and west divisions and take the top three teams from each for the play-offs. Not perfect, but better IMO.
My thought would be to stay with four divisions;
Play the other teams in your division twice;
Play the other conference teams once;
Replace one preseason game with a regular season game, and eliminate the bye week (these two changes would keep the season the same lenght but make it 18 games);
And go into the playoffs with the top team from each division.
No wild cards, and no controversy over easy or tough schedule. Only controversy would be the yearly rotation on who gets homegame and who's on the road for the once a season match ups.
Better yet ... accept it is a game meant for entertainment, and we all put way too much importance on it! The only reason it is big business is because we are stupid enough to give millionare owners our tax money, and pay way too much for tickets to make players into millionares for doing what they paid to play in their youth.