Here's my suggestion - scrap extra time, instead each team splits into a 5 man attack and a 5 man defence. Then play on a half pitch for 10 mins each, and the team that scores more within that time wins. But some problems are:
1. Obviously, what if nobody scores? Should we use stats like possession, shots on goal, shots on target, etc.?
2. How to settle the fatigue issue...if a team has to attack first, they may say they are more tired then the team that gets to attack second who have had a 10 min rest.
What would you suggest if it was in your hands, keeping in mind we want a team aspect to it.