How to make a 16 team conference work

Have four divisions (A, B, C, D) of four teams (1, 2, 3, 4).

Have Div. A play Div. B and Div. C play Div. D (That is four games a piece). The division that you play will rotate every year.

Each team will play the other teams in their division (Three games).

Then each team will play a team that finished in the same place from the division they have yet to play based on the 7 games played thus far. For example, the winner of Div. A will play the winner of Div. C and the winner of Div. B will play the winner of Div. D. Same goes for those that finished 2, 3 and 4, they would play the 2, 3 and 4 ranked teams in the division they have yet to play. (1 game)

The winners of the two first place games will play in the conference championship game. (1 game).

So that is an equal 8 conference games with the winners of the divisional round going to the championship game. This will give each conference as true of a champion as they can get as all teams within a division will be playing the same teams.