One of the problems I would have with your explanation is whether or not Matthew wrote the words in Greek or did he write the words in the original Aramaic. Most Bible scholars believe that Matthew wrote in Aramaic and while Mark's words are almost identical, he too was a Jew who would have spoken a dialect of Hebrew/Aramaic. Psalm 22 renders the word 'azab (or 'azabthani) as "forsaken" in most English versions, however, the word could just as easily mean 'relinquish' or 'permit'.
God did not forsake Jesus on the cross, and both Matthew and Mark would have correctly rendered the Hebrew of Psalm 22. This actually links back to Genesis 22, and Abraham's potential sacrifice of Isaac, a sacrifice that was prevented by the "lamb caught in the thicket"; the language of Genesis 22 bears a striking resemblance to that of Matthew and Mark, in the Aramaic, which unfortunately we don't have now.
Your idea of the thrust of Psalm 22 is on the mark; not one of despair, but one of confidence.
Some of this has been addressed already. See: "Does the phrase "Eli, Eli, lama sabachthani" have a different meaning in Aramaic than in the Greek?" The writers of the New Testament claimed and proved that they wrote by the inspiration of the Holy Spirit. In this case, the translation was given into the Greek by the Holy Spirit:
And about the ninth hour Jesus cried out with a loud voice, saying, "Eli, Eli, lama sabachthani?" that is, "My God, My God, why have You forsaken Me?" (Matthew 27:46).
This verse is one of several in Matthew which shows that Matthew was originally written in Greek. You see, if it was written in Hebrew or Aramaic as has been recently popular to claim, there would be no need to explain Hebrew or Aramaic phrases. Matthew 27:33 is another example. There are times when Matthew does insert Aramaic words without explanation, such as in Matthew 5:22 when he uses raca and allows the context to give the meaning. We also note that Matthew frequently points to the fulfillment of Old Testament prophecies, something that is important to the Jews. Therefore, we conclude that Matthew primarily wrote for a Jewish audience.
However, Matthew's periodic translations of Aramaic and Hebrew phrases and place names tell us that he was writing to a larger audience than just the Jews in Judea. People there would be expected to understand Hebrew and Aramaic. The Jews, however, have been scattered and many spoke other languages (Acts 2:7-11). The one common tongue in the world of that day was Greek, so it is not surprising that the Holy Spirit selected that language for Matthew's account.
Given how rapidly early Christians copied the Scriptures, the fact that somehow no Hebrew or Aramaic version appears until much later and that these translations are obviously done from the Greek text is yet another clue that Matthew was originally written in Greek. Jesus promised, "Heaven and earth will pass away, but My words will by no means pass away" (Matthew 24:35). Despite several efforts to eliminate or restrict access to the Scriptures, they have all failed and I'm confident that this is because God's hand was preserving His word. I believe we have no original Aramaic or Hebrew text of Matthew because none existed -- excepted in the imagination of some today who wish to alter what Matthew said based on this imagined text.
Does anyone have an "autograph" of the book of Matthew? All anyone currently has are texts written some 100 years or longer from the date of the actual record. If you follow the King James Version or the New King James, you reject the ancient texts as being incorrect or misleading. Both the KJV and NKJV follow the Bezae text; I'm sure you already know this.
God has preserved what is necessary for us to be able to determine the truth of His Word. Do you accept I John 5:7, "For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one." (KJV) The more ancient authorities have something that is more like, "And it is the Spirit who bears witness, because the Spirit is the truth." Or, "For there are three that testify:" Followed by verse 8 in the NIV, "the Spirit, the water and the blood; and the three are in agreement."
What we possess of the Word of God is all we really need, but I would challenge anyone to prove that Matthew wrote his record in Greek - I don't know of any legitimate Bible scholar who would assert that as fact. Matthew was Jewish; his record of the birth of the Messiah is for the Jewish people - his record, though inspired by God, was for the Jews. He wrote his record, in all probability, sometime before the fall of Jerusalem. While most believe that Mark wrote his account before Matthew, no one can assert a timeline for either.
We just have to have faith that what is written, in whatever translation we might choose to use, is sufficient for a correct understanding.
I tend to use the NKJV on the web site because more people understand it. It is close enough to the KJV to satisfy people used to reading it but modern enough to be understandable. When I preach, I actually use the NASB. I'm definitely not in the King James Only crowd. See: Which Translation Should I Use?
In regards to proof, I gave you two pieces of evidence, which you haven't addressed. But here are a few other points to consider that I picked up from "Evangelical Textual Criticism." This quote from Dave Black is interesting:
Although I have no a priori bias against an original Hebrew Matthew, I tend to agree with J. Kuerzinger (Biblische Zeitschrift 4  19-38; cf. New Testament Studies 10  108-15) that hebraidi dialekto means "in a Hebrew style" and not "in [the] Hebrew language." In the context of the Papiaszeugnis, the Elder had been explaining some problems in the style and/or content of Mark, since it had neither the Jewish style of Matthew nor the normal literary style of a Greek biography such as Luke's. As I argue in my book Why Four Gospels?, Origen mistakenly thought that Papias was referring to the language of Matthew and stated that "Matthew was composed in Hebrew characters," thus introducing an error that was perpetuated by later writers.
Matthew Black in "An Aramaic Approach to the Gospels" comes to the same conclusion as Dave Black does here - Hebrew or Aramaic language and style in the text doesn't equal Hebrew script for the autograph.
Also from Eric Rowe:
It is not just that Matthew does not have signs of being translated, it also has positive signs of being originally Greek. For example, Jesus' argument in Mat 22:32, when he quotes God saying, "I am the God of Abraham..." depends on the Greek version of Exod 3:6. It seems that Jesus (at least as portrayed in our received Greek edition of Matthew) is drawing a point from the present tense "eimi." But in the Hebrew, it is a verbless clause, from which no such argument about tense could be made, at least not one that would be as plain to the readers of a Hebrew Matthew as those of this Greek version.
I noticed that you hedged your challenge with "legitimate Bible scholar," so I don't know if you will consider these points or not. But regardless of the source, these gentlemen do raise important points that should be seriously considered.