Amen.1) Sin is definitely a debt. The important question is "what is sin a debt of?" Surely, the answer is that sin is a lack of obedience, a lack of love, ultimately to God. It follows therefore that the payment of the debt can only be an act of obedience and love to God. And this is exactly what Paul makes clear in Romans 5:19: “For as through the one man’s disobedience the many were made sinners, so also through the obedience of the One the many will be made righteous.” Jesus’ obedience pays the debt of Adam’s disobedience.
2) My argument does not depend on "became sin" as "became a sin offering" although there is lots of support for that view, even from penal substitution advocates. See Tom McCall in his book "Forsaken" p.23 and 111. And Nathan Busenitz at John Macarthur’s Master’s Seminary, who supports penal substitution himself, says:
““Did Jesus become the literal embodiment of sin, or take on a sin nature, or become a sinner when He died at Calvary?” My answer to that question is a resounding no.”
Busenitz also says that Jesus became a sin offering.
This view explains Paul’s use of the Greek word hamartia (“sin”) which was often used in the Septuagint (the Greek version of the Old Testament) to mean “sin offering.” For example, in Leviticus 4–6, the Septuagint uses the word hamartia more than 20 times to translate the Hebrew concept of sin offering. Paul’s frequent use of the Septuagint means he would have been familiar with using hamartia in that way.
Busenitz then quotes the church father Abrosiaster:
Ambrosiaster: “It was only because all flesh was subject to sin that He was made sin for us. In view of the fact that He was made an offering for sins, it is not wrong for Him to be said to have been made ‘sin,’ because in the law the sacrifice which was offered for sins used to be called a ‘sin.‘ (Commentary on Paul’s Epistles, cf. Ancient Christian Commentary on Scripture, 7:252)
Did Jesus Become a Sinner on the Cross? - The Cripplegate
I think it most important to see "became sin" as Jesus becoming a demonstration of all our sin. We cannot understand human sin in its fullness until we look at how we treated Jesus. All of our sin was poured out on him there. All of our sins are contributions to his crucifixion. The same way we might say that "Whipped Peter," depicted in the famous photograph, became America's sin with regard to slavery. The symmetry of the verse is that "God demonstrated the fullness of our sin through the sinless one, and He demonstrated the fullness of His covenant faithfulness through those who had been faithless (the church)."
I'll add that nobody actually believes Christ became literal sin (even those who argue against using "sin" to mean "sin offering" provide a less than exact meaning for the word).
And it really does not matter in terms of the argument at hand.