2 Corinthians 5.20 is an interesting scripture to bring forth. It poses some difficulty to translate it correctly. I find that most translators have to add or take away some words within the text to have smooth English. But one issue where translators depart in the text is in the translation of the Greek preposition "hyper" which appears twice. As is often the case, prepositions can have many meanings, so interpretation plays a major role in the translation process.
"Hyper" generally means "over" (opposite of hypo, "under") but has been translated variously: for; about; in; above; beyond; for the sake of; more than; on behalf; concerning; for sake; on behalf of; over, than; to, etc.
In compounds with verbs, nouns, or adverbs it adds the ideas of:
(1) over or beyond, spatially; (2) for someone or something; or (3) beyond (normal) limits.
Some believe that in 2 Cor. 5.20, the idea of "substitution" is brought out by the fact that the preposition used here, is also used 6 other times in the chapter. See 2 Cor. 5.15 & 21, for example.
Paul, is, within this context, defending his apostleship, his authority as God's representative. Which is why, he uses "hyper" as the first word for emphasis in the text, for what Paul has to say in his defense. Paul was conveying that he was a messenger of God, an ambassador. In the absence of Christ, he was serving in his place (as a "substitute") to appeal to them as if God himself was making appeal to them through him: "As God's ambassadors, we beg: Become reconciled to Christ." Hence, Paul had the "authority" to be the apostle of God and Christ, which church infiltrators questioned.
Greek Grammar Beyond the Basics says under "Hyper": "It is our conviction that ["hyper"] is naturally suited to the meaning of substitution and is in fact used in several passages dealing with the nature of Christ's atonement." (p. 383)
Kenneth S. Wuest, in his literal translation, makes an effort to bring out the Greek meaning of what Paul was saying:
"Therefore, on behalf of Christ and in His place we are acting as ambassadors, as though God were saying, I beg of you, please, through us as His intermediate agents. We beg you in Christ's stead, Be reconciled at once to God " (The New Testament - An Expanded Translation)
The idea of "substitution" in the text within Paul's context, is not so absurd after all. The problem is that some religious groups, like the JWs and the Catholics, use Scripture to enforce their authority on their followers beyond what the Bible demands of Christians.
Because of this, I prefer this reading from the Simple English Bible:
"We are representing Christ. It is as though God is encouraging you through us. We beg you, for Christ's sake, come back to God!"