That's the one. I posted years ago a suggestion that NFL start mixing things up with teams. Adding an annual "NFL Draw" event would be great hit for them and generate more eyeballs and attention that so-called rivalries. Something similar to event like UEFA Champions League Draw, World Cup Draw and so forth.
No one cares about rivalries that much, although, the new NFL Draw would still put traditional rivals in the same division.
Keep the divisions format with two conferences, at the end of the season, rank teams in 4 levels and each division would get one team from each level. Imagine the anticipation of who our division would be, who would we be facing outside the division, outside the conference, etc.
Someone like Jerry might be against it since his Cowboys would lose trips and coverage from big markets like NY, PHI, and DC. But hey, you are looking for fresh ideas, $$$ generation, excitement, and, I would say, more fair team alignment.