Christ 'made' sin - the Reformed, Protestant view?

It is true that very often Harmartia is used to mean sin or offence in the new testament. It could be exactly what Paul means in 2 Corinthians 5:21 as well, even though this has caused no small difficulty in understanding down through the centuries for individuals as much as for entire theologies. There are so many references to Jesus taking away sin, suffering for our sin, condemning sin in the flesh, etc. To my knowledge this is the only place that looks like it is being said that God made Jesus to BE sin and just that alone should raise some eyebrows...and it has!

But there is another possibility that so nicely harmonizes with the rest of scriptural revelation that it is hard to ignore. In the Septuagint in Exodus, Leviticus, and Numbers the Greek harmartia is used over 90 times where the Hebrew text has 'sin offering'. Since the Septuagint was written 250 years prior to Christ it is entirely possible that the Corinthians were familiar with it. After all, Paul would usually go first to the synagogue with the gospel and there were certainly Greek speaking Jews in Corinth. Often, when the New Testament refers back to the Old, it pulls from the Septuagint and this could easily be one of those times. If so then Paul is saying that "God made him, who knew no sin, to be a sin offering for us" and this takes away all the theological angst. Below is a part of Adam Clarke's commentary:

For he hath made him to be sin for us - Τον μη γνοντα ἁμαρτιαν, ὑπερ ἡμων ἁμαρτιαν εποιησεν· He made him who knew no sin, (who was innocent), a sin-offering for us. The word ἁμαρτια occurs here twice: in the first place it means sin, i.e. transgression and guilt; and of Christ it is said, He knew no sin, i.e. was innocent; for not to know sin is the same as to be conscious of innocence; so, nil conscire sibi, to be conscious of nothing against one's self, is the same as nulla pallescere culpa, to be unimpeachable. In the second place, it signifies a sin-offering, or sacrifice for sin, and answers to the חטאה chattaah and חטאת chattath of the Hebrew text; which signifies both sin and sin-offering in a great variety of places in the Pentateuch. The Septuagint translate the Hebrew word by ἁμαρτια in ninety-four places in Exodus, Leviticus, and Numbers, where a sin-offering is meant; and where our version translates the word not sin, but an offering for sin. Had our translators attended to their own method of translating the word in other places where it means the same as here, they would not have given this false view of a passage which has been made the foundation of a most blasphemous doctrine; viz. that our sins were imputed to Christ, and that he was a proper object of the indignation of Divine justice, because he was blackened with imputed sin; and some have proceeded so far in this blasphemous career as to say, that Christ may be considered as the greatest of sinners, because all the sins of mankind, or of the elect, as they say, were imputed to him, and reckoned as his own.

Also from the Benson Commentary:

For he made him, who knew no sin — A commendation peculiar to Christ; to be sin — Or a sin-offering rather, (as the expression often signifies both in the Old Testament and the New;) for us — Who knew no righteousness, who were inwardly and outwardly nothing but sin, and who must have been consumed by the divine justice, had not this atonement been made for our sins; that we might be made the righteousness of God in him — Might be accounted and constituted righteous by God, or might be invested with that righteousness; 1st, imputed to us; 2d, implanted in us; and, 3d, practised by us; which is, in every sense, the righteousness of God by faith. See note on Romans 10:4; Php 3:9.

Barnes' Notes On the Bible:

For he hath made him to be sin for us - The Greek here is, 'for him who knew no sin, he hath made sin, or a sin-offering for us.' The design of this very important verse is, to urge the strongest possible reason for being reconciled to God...To be sin - The words 'to be' are not in the original. Literally, it is, 'he has made him sin, or a sin-offering' ἁμαρτίαν ἐποίησεν hamartian epoiēsen

Matthew Poole's Commentary:

Our sins were reckoned to him; so as though personally he was no sinner, yet by imputation he was, and God dealt with him as such; for he was made a sacrifice for our sins, a sin offering; so answering the type in the law,