How about 7 teams going 14-2 spread across one conference?  I believe that is possible too.  Take DAL-PHI, MIN-GB, NO-ATL, and ARI.  Assume NFC-E is matched against NFC-S.  DAL & PHI split their games and sweep the other four divisional games.  Both must play NO & ATL, so they split those games as well.  Thats two losses for everyone.  They avoid playing the teams mentioned above in the one game they need to play against the NFC-N & NFC-W, and they sweep AFC opponenets.  Its a stretch but possible, unless I missed something.