Here's a Coptic Orthodox fraction to God the Son said at any point in the year. The lyrics are interesting in that they do teach that Christ satisfied the Divine Justice (albeit, it probably uses the "Divine Justice" terminology with an intent different than that of Anselm). What do you all think?
O only-begotten Son, God, the Logos who loved us, and through His love, He desired to redeem us from eternal perdition.
And since death was in the way of our redemption, He desired to go through it out of His love for us. And thus, He ascended upon the Cross that He may bear the punishment of our sins.
We are the ones who sinned, and He is the One who suffered.We are the ones who were indebted to divine justice because of our sins, and He was the One who paid off the debts on our behalf.
For our sake, He preferred suffering over joy, toil over rest, contempt over glory, and the Cross over the throne which is carried by the cherubim.
He consented to be tied by ropes that He may loose us from the bonds of our sins. He humbled Himself that He may lift us up. He hungered to satiate us, and thirsted to quench our thirst.
And He ascended upon the Cross naked that He might clothe us with the garment of His righteousness. And He opened His side by the spear that we might enter into Him and dwell in the throne of His grace, and that the Blood might flow from His Body that we might wash ourselves from our iniquities.
Indeed, He died and was buried in the tomb, then He arose that He might raise us from the death of sin, and give us life unto life eternal.
My sins, O my God, are the thorns that pierce your holy head; I, who have saddened Your heart by my rejoicing in the vain pleasures of the world.
What is this road that leads to death in which You are walking, O my God and my Savior?
What is it that You are carrying upon Your shoulders? This is the cross of shame which You have carried on my behalf.
What is this, O Redeemer? What has caused You to consent to this?
Shall the Great One be despised? Shall the Glorified One be afflicted? Shall the Exalted One be humbled? Oh! The greatness of Your love.
Yes, it is Your great love that made You accept with endurance all these sufferings for my sake.
I give thanks to You, O my God, and Your angels, with all Your creation, give thanks to You on my behalf, for I am unable to present Your praise as befits Your love. Have we ever seen a greater love?
So be sorrowful, O my soul, for your sins that caused these sufferings to Your compassionate Redeemer. Portray His wound before you, and hope in Him when the enemy rages against you.
Grant me, O my Savior, to consider Your suffering my treasure, the crown of thorns my glory, Your sorrows my joy, Your bitterness my sweetness, Your blood my life, and Your love my pride and my thanksgiving.
O my Lord Jesus Christ, who was wounded on account of our sins, and by Your bruises we were healed, wound me by the spear of Your healing divine love. And by the blood of your Cross, purify me from my sins. Cheer me also by Your love, O You who accepted death for my sake, that You may redeem me and give me life.
O my Lord Jesus, my beloved, if You see me as a withered organ, soften me with the oil of Your grace, and confirm me in You as a living branch, O true Vine.
And when I come forth to partake of Your mysteries, make me worthy of Them, and fit for communion with You, so that I may dare with boldness without fear to call on Your holy Father, who is in the heavens, with the voice of children, saying, Our "Father ...."http://tasbeha.org/hymn_library/index.php?a=view&id=2473