It claims that Jesus' sacrifice redeemed the world, but as far as I can see, self-sacrifice doesn't generate much beyond fodder for guilt trips.
You're taking an event where one person sacrificed himself for others and applying it to a discussion about suffering for your own benefit (or not). Jesus' sacrifice didn't redeem the world because of some generic payment-for-suffering karma. It redeemed the world by bringing to completion the sacrificial system under Mosaic Law; you can't discuss Jesus without referring to Moses.
Self-sacrifice for Christians is a response to that, not an attempt at payment. If there's any payment involved, it's in the other direction: me trying in my own small way to give back to God what he gave me. Small but meaningful.
It's difficult to discuss this with you, since you are a lot like me: we tend to believe any trouble in our lives is the result of either misunderstanding or bad timing--something to do better next time, but not anything that needs forgiveness. Most of the time this is true; I try to do what I believe is right. In this context, I couldn't agree with you more about redemption and forgiveness (although working with parties who ascribe malice where there was only ignorance can throw a wrench in the works).
However, that's not the context of which I'm speaking (above). I'm talking specifically about those times in our lives when we know what is right and yet do something else. People expect relational recompense for that, usually in the form of ceremonial humility, by choosing to lose face or material goods or ...? Symbolic, perhaps, but no less necessary for that. In the agreement God made with Moses and his people, you were expected to sacrifice animals to this end, as a symbol of your acknowledgement of wrongdoing and your desire to work toward reestablishment of the agreement whose terms you broke. Jesus died as the final, all-encompassing sacrifice in this chain, bringing to a close that agreement (since its terms were now fully satisfied) and bringing into existence a new one. It's much more a legal, contractual issue than a metaphysical or even behavioral one.