If I was commissioner, here's what I would do.
You make the field 70 yards long, but you have two fields in parallel. You then connect them with curves in the end zone to make the thing a big race track. If a guy scores standing up, he keeps running around the track. He gets more points for getting around the curve and reaching the second field, and even more points if he can traverse that entire field. He keeps going until someone finally brings him down. If he can make it fifty laps, his team is racking up points like a pinball machine.
Now, the defensive team can choose to chase the guy, or they can run around in the other direction to stop him on the other side. If a guy is really fast and he scores, some of the defenders may chase him and others will run the opposite direction so they can stop him on the next lap. Maybe you even have a rule where the defenders can throw another guy on the field every time an endzone is crossed.
It would be loads of fun.
My ancestors fought cave bears so I could make this post.