Love the idea of an eight team double-elimination tournament - anything that reduces luck and rewards good teams is a good idea IMO.
Unfortunately it can take as many as six games to decide the winner. And it always takes at least five.
That's correct. You can see a double elim. 8 team seeded bracket here:
8 Team Seeded D.E.
However, with double headers you could make it considerably shorter. You could base the 2nd game of the double header bracket on the result of the first game (i.e. like they were played one after the other instead of simultaneosly). The problem with that is you really aren't minimizing luck - if a team had a good week (or bad one) - they'd win both games (or lose both). So realistically, given the current NFL schedule, limited number of games, etc. I don't see how this possible from a practical standpoint.
Obviously, an 18 game schedule could make it possible. But keep in mind that with an 18 game schedule, the chances that a team will have the division (or wildcard spot) locked up early is probably a greater possibility (i.e. "Colts Syndrome") - especially if most of the other teams within a division are poor. This season is a poor example of that.