My solution for the NFL OT, the 2-minute drill (How all good games should end.):
1. Coin toss. Winner of the coin toss can elect to go first or second.
2. 2:00 minutes placed on the clock and 2 timeouts given to Team A.
3. Kickoff. (1st OT session can only be ended by a score or time running out. *No 2-point conversions allowed. If a turnover occurs, the team that caused the TO can use the remaining time to score and win the game.)
4. 2:00 minutes placed on the clock and 2 timeouts given to Team B.
5. Kickoff. (2nd OT session – Team B MUST go for the win. No tying FG will be allowed. A tying TD must be followed by a 2 point conversion. )
6. Repeat if neither team scores.
I think this employs strategy and excitement for the overtime period, both of which are currently absent in the current format.