Taking the luck factor out of team schedules
I would like to propose a league option where you have the ability to go 2-0, 1-1 or 0-2 on the week. You would get 1 win for head to head and 1 win if you are top 50% in scoring for the week.
For instance, in my league, there is a team that is the "points for" leader and the points against leader by a wide margin. This team is "1-5" due to bad luck due to their schedule.
This team has been a top 50% scorer in 5 out of the 6 weeks. With this change, they would be a 3rd place team and more reflective of how good their team is.
This idea doesn't solve much. Your example team would be 6-6 with your change. That still doesn't reflect the record that the "points leader" should have. How can a 6-6 team be in 3rd place in your league? Does your league have just six teams in it?