Let's Talk Tie Breakers!

As reported in the previous post, last night's titanic struggle ended in a 0-0 tie.  After the final swing and a miss, the five of us present tried out a possible tie breaking rule to see what we thought.  Well, we sorta tried the rule.  Certain aspects of the rule were changed by Peter using his "Best Interests of Whiffle" powers. For starters, Peter declared that this was a test and that the tie result would stand.  Here's how the "Toss Up Tie Breaker" went:

1. First the teams were made even as the game was played three against two.  Matt proposed that the team with three should go with the next two batters due up in the order (which would have been Glen and Kurt) so that the choice of who sits is random.  Peter announced that the team could simply choose which player would sit out.  Kurt chose not to participate because he disliked the idea entirely (more on that at the end).
2. Matt announced the following rules: Starting with the visitors, each player was to take the ball and bat, choose either batter's box to stand in.  The player will toss the ball up for themselves and take a swing attempting to hit a homerun.  The player may have as many tosses as they need, but ONLY ONE SWING.  Each visiting player shall take his/her swing, and the total number of homeruns hit shall be recorded.  Once all visitors have swung, the home players shall swing by the same rules.  The team with the most total homeruns shall be declared the winner of the Whiffle game.  Peter changed this to be the person who hits a ball the farthest shall win the game for his/her team.  Glen swung first and very smartly hit a ball up the middle (shortest distance to the homerun line), which landed a few inches shy of the triples line.  Tim then had a swing and a miss.  Matt then had a swing and a miss.  Peter then struck a high fly ball, pulled down the third base line that landed just inches shy of the triple line.  Glen and Kurt agreed that Peters was closer to the triples line, and that therefore under Peter's rule Peter had won the game.
3. Under Matt's original rule, with no homeruns hit, a second round would have been played, and so on until at the completion of a round one team had more HR than the other.  An un-encountered issue this evening was whether the team with three would use the next two due up, or the same two in every round.

After that was done, Kurt decided to get in on the fun and tried his luck.  One toss; one swing.  Kurt hit a booming shot well past the homerun line, which would have won the test for his team under any set of rules.

So, here are the questions to be answered:

1. Does the League need a tie breaking rule?
2. Are "Toss-Ups" a good method for settling ties?  If not, what do you propose?
3. What specific rules should govern the tie breakers?
4. How should performance in the tie breakers be reflected in the LEAGUE stats?

Let's get the debate going in the comments.