According the wikipedia article on rule sets' treatment of the end, all the sets actually say that you should play things out, capturing dead stones.

No, it's only the Wikipedia rule set which says this. Then the article says

Rule 9 differs significantly from the various systems for ending the game used in practice

So none of the rule sets used in practice agree with Wikipedia's Rule 9.

That true for some Go rule sets but it isn't true for Japanese style rules.

This is from lower down on Wikipedia (more there):

However, under Japanese rules, the game is already considered to have ended. The players attempt to ascertain which groups of stones would remain if both players played perfectly from that point on. (These groups are said to be alive.) In addition, this play is done under rules in which kos are treated differently from ordinary play. If the players reach an incorrect conclusion, then they both lose.

So if neither player is good at distinguishing live from dead, then both may lose! (So much for a zero-sum game.) I am not fond of this feature of the Japanese rules; I much prefer the idea that one solves disagreements by playing them out. But then I am an even weaker player than you, so what do I know? (^_^)