The Count: I don't think I was specific enough in my rationale for why the game should end – this "no more worthwhile moves" idea. Defining the idea is very difficult. For example, in a double-ko seki, the player who tries to cause endless repetition thinks their moves are worthwhile because they can cause a "no result". If the rules are such that this is not true, then playing in the double-ko seki is not worthwhile. The rules determine what is worthwhile, and so what is worthwhile cannot be used to determine the rules. I believe the following precisely analyses the game end condition.
If there were no stopping rule at all, eventually an endless cycle would occur (if we assume that a player would do the same thing in the same situation every time it occurs). For the duration of the cycle, one of the following would have to be true:
 An NSC pass is a non-situation-changing pass. If passes lift ko bans, this means a pass when there are no restrictions due to ko. If passes don't lift ko bans, this is just a normal pass. Sorry to introduce this silly terminology, but I think it's necessary.
So in a normal game of go, a point is reached where both players would keep on alternately passing if the game did not end. This meets (3aa) above. Clearly, the game does tradiationally end when (3aa) is met. As for why, there is the argument that if (3aa) is true, the score is "constant" and so the game should end. By this argument, it would be reasonable to not assign a score for (3ab) or for anything other than (3aa). We can't really say why the game ends, we can only say the game does and must end in one particular situation, (3aa).
If (1) is true, it would be silly to assign a score. Traditionally, the game doesn't end. This is like if a triple ko occurs. So the stopping rule should be such that is doesn't assign a score.
For all the other situations, just like for (3a) and (1), there is no principle that can be used to determine what should happen. If (2a), we could reasonably either make the game stop with the score of the position(s) that was (were) passed in, or make the game stop with no result. For (2b) and (3b) we might average the scores of the various positions, but this is no doubt too complicated to be desirable for such rare positions if they even exist.
To conclude, all we can say for sure is that a stopping rule must give the traditional score for the cases (3aa) and (1). However, we might like to use the "constant score" argument to allow the game to end only for the case (3aa). What do you think?