I wouldn’t say mangled. I’d say that I have adjusted my understanding of the atonement to fit the historical contours of scripture. We can say that Jesus died for our sins, or for the sins of our neighbours, or for the sins of the world. But there’s a backstory to that.
Jesus’ death needs to be understood against the background of the dawning realisation that the suffering of righteous Jews, at the hands either of the powerful and unrighteous in Israel or of pagan oppressors, could have atoning effect. In the first place, therefore, Jesus died as a righteous son of God for the sins of Israel, so that God’s people might have life and a continuing missional purpose after the catastrophe of the war against Rome.
Secondly, this death for the sins of Israel had a somewhat unexpected consequence. Because after Pentecost the Spirit was poured out on those who believed that God had raised his Son from the dead, not on those who were keeping the Law, it became apparent that there was nothing to stop Gentiles believing and receiving the Spirit. To cut a long story short, the death of Jesus had the further effect of removing the dividing wall of the Law: because Jesus died for the sins of Israel, Gentiles were also forgiven and embraced within the covenant community.