God's wrath is a part of God's righteousness. God's wrath is personal but it is not arbitrary or capricious anger. Paul does not speak about the faith of Christ but rather about faith in Christ. An Anselmic reading of this text is the correct one. Hilasterion refers to the mercy seat.
Redemption involves the payment of a price.
When Paul, in Romans 5, speaks about our being saved by Christ's life, he is referring to Christ's intercessory work for believers. When Adam sinned, death entered the world and engulfed all people. Hence all people enter the world alienated from God and spiritually dead by virtue of Adam's sin. So Paul not only claims that people die because of sin but also that they sin because they are dead. The focus in Romans 6 is not on the penalty of sin but on its power.