Added a new link to Nailbiter Games. Nailbiter Games specializes in sports sims. I've downloaded a couple and they look very interesting.
These games are not in the Statis-Pro or APBA category. Each game is an abstraction that looks at the relative strengths of two teams and provides highlights of each drive.
One game, however, allows for a distribution of points to a team's roster. It is called Coach's Call Football and is avaiable here. QB's have a cost, the better rating, the more costly. Skill positions have a cost. The Defense is a generic rating, but you can rater the DL and LB on a 1-5 scale. The same is true of the OL.
It wouldn't be hard to imagine using this system to rate all the teams and recreate a season. Just may have to fiddle with it and see what turns up.
This game is chart-heavy. This doesn't bother some folks, but I thought it would be fair warning for others that may not like a game with seven results charts.