LSU wasn't a better team than USC or Oklahoma that year, nor did they have a better record than an undefeated USC or Oklahoms. That was the USC/Oklahoma/Auburn/Utah (I think there was a fith team too, possibly Boise State) undefeated at the end of the season so who will go to the NC debacle, much like this year.
Everything else in your post I agree with except I think a playoff of 8 would work better. I almost like the old bowl system where you could suddenly be playing for the National Championship in the middle of your bowl, because #1 whoever just fell to #6 whoever in their bowl.