This is something I would like to dig into more myself. However, I do think that it is incorrect to view forgiveness through Christ as justice. Justice would be getting what you deserve, justice would be death. Forgiveness is a mercy, and mercy transcends justice.
James 2:12-13 So speak and so act as those who are to be judged by the law of liberty. 13 For judgment will be merciless to one who has shown no mercy; mercy [m]triumphs over judgment.
I would also say that it is incorrect to assert that because of Christ that God now has the ability to forgive sin. He has always been willing to forgive one who repents earnestly. Take a look at David, for instance, who clearly deserved death for his transgressions. Rather, scripture says that Christ was given the authority to forgive sins from God - even before his sacrifice.
Matthew 9:5-8 Which is easier, to say, ‘Your sins are forgiven,’ or to say, ‘Get up, and walk’? 6 But so that you may know that the Son of Man has authority on earth to forgive sins”—then He *said to the paralytic, “Get up, pick up your bed and go home.” 7 And he got up and [c]went home. 8 But when the crowds saw this, they were [d]awestruck, and glorified God, who had given such authority to men.
It is also not the case that either sin or death for it are completely done away with, at least at this point. Rather, we must die and be born again. I think this to be a more accurate understanding of what Christ's death accomplished: that just as he died, we must die - and as he rose, so too will we rise. It is the New Covenant which was established with Christ's blood - so that everyone be afforded the opportunity, the right, to become children of God.
Romans 8:3 For what the Law could not do, weak as it was through the flesh, God did: sending His own Son in the likeness of [c]sinful flesh and as an offering for sin, He condemned sin in the flesh
1 Corinthians 15:21-22 For since by a man came death, by a man also came the resurrection of the dead. 22 For as in Adam all die, so also in [h]Christ all will be made alive.
Luke 22:20 And in the same way He took the cup after they had eaten, saying, “This cup which is poured out for you is the new covenant in My blood.
Hebrews 9:16-17 For where a [q]covenant is, there must of necessity [r]be the death of the one who made it. 17 For a covenant is valid only when [t]men are dead, for it is never in force while the one who made it lives.