There has to be a better way. I think the way college does it, creates a situation of prolonged games like this. I don't like sudden death either.
I think adding a certain amount of time on the clock (10 min) and playing it like it is the start of the game. Coin toss, kick off, etc. Give each team 1 timeout.
I know there would need to be some semantics worked out, but that seems plausible.
For time constraints. Allow each team to line up on the 20 and kick field goals. Back it up 10 yards after each team has the opportunity to make one. After 50 yards move it at 5 yd increments. It would suck to lose a game like that, but would be entertaining.