"Sin" in 2 Corinthians 5:21

I've been doing a study on 2 Corinthians 5:21, specifically about the odd saying that "God made him who had no sin [i.e. Jesus] to be sin for us". This verse has traditionally been interpreted to mean that by some mystical transference God turned Jesus into sin during the crucifixion in order to be substitutionally punished for the sins of humanity. However, I had noticed that several of the better, scholarly translations of the New Testament add a footnote to the second occurrence of "sin" (hamartia) in verse 21, indicating that it can be translated as "sin-offering".

The reason for this is that the Old Testament uses the same word (chatta'ath) for both "sin" and "sin-offering". Only contexts determines the usage.

Therefore, we get a translation of Leviticus 4:3: "If the anointed priest sins, bringing guilt on the people, he must bring to the Lord a young bull without defect as a 'sin offering' [chatta'ath] for the 'sin' [chatta'ath] he has committed."

Now when the Hebrew Bible was translated into the Greek Septuagint (LXX), the translators rendered chatta'ath as hamartia.

With this in mind, the  atonement context of 2 Corinthians 5:21 suggests that Paul intended the second use of hamartia to be understood as "sin-offering" instead of "sin".

It makes more sense to think of God considering the sin-less Jesus an offering for sin than actually somehow turning him into sin.