Your explanation of the above subject is a bit confusing because we are told that the Old Testament was translated from Hebrew to English while the New Testament was translated from Greek to English. So, I expect them to pick the pronunciation of the same words uttered before translation into English or any other language.
In the United States, we have several dialects of English. I can write down what a Southerner says in the way it is pronounced: "Lem-me put mah feet up - Aah'm taard." Or, I can write the same statement with the standard English spelling: "Let me put my feet up - I'm tired." Both are accurate but serve different purposes.
Matthew recorded how the words of Jesus on the cross were pronounced because he was demonstrating why the crowds thought Jesus was calling for Elijah. Mark recorded Jesus' words as they were properly spelled. But both were writing in Greek, so they had to use Greek letters to get close. Jesus spoke in Aramaic on the cross. His words were then transliterated into Greek; that is, Greek letters were used to approximate what Jesus said. However, not there is not a one-to-one correspondence between Aramaic sounds and Greek sounds.
The answer "Why does Mark have “Eloi” and Matthew have “Eli” for the same statement?" gives the details.
Please, the difficulty with the explanation you have given is that both Matthew and Mark are claiming what Jesus said verbatim. Using the King James Version (KJV), let me explain my view.
"And about the ninth hour Jesus cried with a loud voice, saying, Eli, Eli, lama sabachthani? that is to say, My God, my God, why hast thou forsaken me?" (Matthew 27:48).
"And at the ninth hour Jesus cried with a loud voice, saying, Eloi, Eloi, lama sabachthani? which is, being interpreted, My God, my God, why hast thou forsaken me?" (Mark 15:34).
From the above two quotations, both authors are laying claim to the vowels of the sounds from the mouth of Jesus. The question is, did Matthew hear "Eli", while Mark heard "Eloi"?. We should also not forget that Mark told us in the bible that at the critical moment of Jesus, "And they all forsook him, and fled (Mark 14:50, KJV).
If Mark 14:50 is to be the case, then it means both Matthew and Mark were basing their stories on hearsay from other people because they were not there to hear verbatim from the mouth of Jesus uttering these words. Hence, the difference in what each claimed to have heard from supposed eyewitnesses.
Note: The author continued with a long note getting further and further off-track from his original question, claiming that the Bible is unreliable because it talks about the sins people committed, as if mentioning facts was supporting the sins committed. In doing so, he demonstrates an unwillingness to distinguish what people did versus what God required of men.
I delayed answering because it is clear that no answer would be adequate for you. It isn't that either answer was difficult to understand. You merely use the claim of not understanding as a launching pad for spreading doubt.
It is well-known that people in the past did not use the same rule regarding quotations that we do in our modern society. To them stating what another person said, even if minor changes are made to tense or wording was done to fit what is being said currently was still considered a quotation. Your first flaw was claiming that Matthew and Mark said they were quoting Jesus verbatim. They each only said that this is what Jesus said. You added a stricter demand on the quotation that neither claimed. Not content with this, you then claimed that they both were quoting Jesus phonetically. Again, this is your claim and not what either writer said. Then you pretend you are upset because Matthew and Mark are not phonetically the same. You only proved that your claims were false. You failed to prove that Matthew and Mark did not tell us what Jesus said.
Your third line of attack was to claim that Matthew and Mark weren't there by quoting Mark 14:50. Yes, the disciples fled when Jesus was arrested. But we know from the accounts that both Peter and John attended the trials (Matthew 26:58; John 18:15). We also know that some of the women disciples and John were nearby when Jesus hung on the cross (John 19:25-27). While others are not specifically named, it would not be surprising that Matthew and Peter were also there but in another location. Again, you claim they were not eyewitnesses, but you failed to prove your point. Assertions are not evidence.