Our Lord was not merely a substitute but a sacrificial Lamb sent by God to take away our sins. He is a redeemer; one who purchases us from death and the grave by paying the price of our release with His sinless life unto death. He died because of/for our sins.
God's punishment for sin is death. The justice and mercy of God is shown that He sent His own Son to die as a Redeemer of mankind by offering His sinless life as a sacrifice and dying for our sins. God Himself judicially "has laid on him the iniquity of us all"; meaning, God judicially applied the guilt of our sins to His Son's sacrificial death, thus judging everyone's sin in the bodily sacrificial death of our sinless Lord.
You cannot find anywhere in the bible that Jesus was punished by God. You cannot. What you find is Jesus offering up Himself to die as the sacrifice for our sin; that in His death the guilt of our sins are judicially applied, thus effectively taking/carrying them away.
What you find is God's merciful grace fulfilling both His justice and mercy. Justice that a death for our sin has occurred, and mercy that He permitted a sinless person's sacrificial death for our sins to be the means to judicially render judgment for our sin, resulting in our justification to eternal life to be received simply by believing...This is what you find illustrated in the OT and fulfilled in the NT.
"Therefore he is the mediator of a new covenant, so that those who are called may receive the promised eternal inheritance, since a death has occurred that redeems them from the transgressions committed under the first covenant." (Heb 9:15)
"For if by the one man's offense death reigned through the one, much more those who receive abundance of grace and of the gift of righteousness will reign in life through the One, Jesus Christ. Therefore, as through one man's offense judgment came to all men, resulting in condemnation, even so through one Man's righteous act the free gift came to all men, resulting in justification of life." (Rom 5:17-18)
You stated, "
The way Christ saves us is by carrying out justice for our sins, not by ignoring them." This is dogma speech and not accurate to the biblical record. Jesus Christ our Lord was the Lamb of God who took away our sins in His death, while it was His Father that carried out justice and mercy in the sacrificial death of His Son, as explained above.
God Bless