Sorry Joe,
This falls under the category of nice try, but epic fail.
The reason is simple, you fail to examine parallels, and again you fail to consider Matthew as the direct source. And do not in anyway eliminate it as a source. This allows me to throw an avalanche of evidence against it. Here is just a quick summation of why these verses blow up in your face.
Mark 13:5-6 is in fact paralleled by Matthew and Marcion (Luke in Marcionite form)
Matthew 24:
[4] And Jesus answered them, "Take heed that no one leads you astray.
[5] For many will come in my name, saying, `I am the Christ,' (Ἐγώ εἰμι ὁ χριστός) and they will lead many astray.
Luke 21:8 (Marcionite form, per Tertullian ):
for many will come in my name, saying, `I am Christ!'
πολλοὶ ἐλεύσονται ἐπὶ τῷ ὀνόματί μου λέγοντες, Ἐγώ εἰμι ὁ χριστός.
Venient ... illi dicentes, Ego sum Christus (AM 4.39.2)
The exact same argument is made in Matthew which would have been known to John. And in Matthew (and Marcion) it specifically refers to claiming to be the Christ. This renders Mark 14:62 somewhat moot.
But if we look at the denial parallels we see John is follows Matthew and Marcion
Matthew 26
[63] But Jesus was silent. And the high priest said to him, "I adjure you by the living God, tell us if you are the Christ, the Son of God."
[64] Jesus said to him, "You have said so (Σὺ εἶπας).
But I tell you, hereafter you will see the Son of man seated at the right hand of Power, and coming on the clouds of heaven."
Luke 23
[3] And Pilate asked him, "Are you the King of the Jews?" And he answered him, "You have said so." (Σὺ λέγεις)
The Marcionite (AM 4.42.1) however matches Matthew:
Pilato quoque interroganti, Tu es Christus? proinde (respondisse), Tu dicis
Pilate asked him, "Are you the Christ?" And he replied, "You say that I am" (Σὺ λέγεις)
Now let's look at John's version of the trial question from Pilate
John 18
[33] Pilate entered the praetorium again and called Jesus, and said to him, "Are you the King of the Jews?"
...
[37] Pilate said to him, "So you are a king?" Jesus answered, "You say that I am a king. ..." (Σὺ λέγεις ὅτι βασιλεύς εἰμι)
In my model, Luke has taken the King of the Jews from John, while Matthew and Marcion had the same source asking if he were Christ. Mark has changed it to the active affirmative instead of the passive "you say I am", perhaps drawing from Marcion (version of Luke 21:8) and Matthew 24:5. But in any event Mark makes an advancement of theology of Jesus' response at the trial to a more open "I am (the Christ)". But John does not know this affirmative response to the question of Jesus declaring himself Christ, he only knows the non responding Jesus who simply says "you say so."
This is of course the the direct response to the trial. You have displaced the response it to an unlikely place, the questions in chapter 8 about Abraham's relationship to Jesus and the Jews. This would be unusual. And John 8 seems to me to be a development of the Gnostic theology where Christ is pre-existing (a theme throughout John, e.g., 1:1-14, 17:24, showing how far removed John's sect is from the Marcionite theology) and about Abraham's two children as presented in the Marcionite version of Galatians (reverses Ishmael and Isaac).
You also refer back to verse 8:17 '
In your law it is written that the testimony of two men is true;' as the source of the invoking of the father as a 2nd witness in 8:54 (as if Jesus doesn't do this throughout John). But you miss the most important aspect of that verse, Jesus statement that the Law (books of Moses) is the Jew's but NOT his. He state's the code, but it is done so in mockery of the Law of Moses (John 1:17), not in response to Mark's claim before the Chief Priest.
Now getting back to your statement about special Markan language. But frankly it's not. Ἐγώ εἰμι in one form or another occurs over 90 times in the NT, but only 4 of these occur in Mark, all with parallels. Even Mark 14:62 appears to most closely echo Luke 22:70
Luke 22
[70] And they all said, "Are you the Son of God, then?" (Σὺ οὖν εἶ ὁ υἱὸς τοῦ θεοῦ;)
And he said to them, "You say that I am." (Ὑμεῖς λέγετε ὅτι ἐγώ εἰμι.)
This verse is attested to identical in Marcion in AM 4.41.5 Ergo tu filius dei es? ... confirmative respondit; et adeo sic fuit pronuntiatio eius
As for Jesus using the "magic words" ἐγώ εἰμι, well that occurs all over the place, and contextually for identity in verses:
4:26, 6:35, 6:41, 6:48, 6:51, 8:12, 8:18, 8:23, 8:24, 8:28, 8:58 (your verse Joe), 10:7, 10:9, 10:11, 10:14, 11:25, 14:6, 15:1, 15:5, 17:14, 17:16, 18:5, 18:6, 18:8. Jesus also uses it to signify his movement, his coming and going in several verses. In John's Gospel we also see John the Baptist use the phrase in denial in verse 1:20 and repeated by the narrator in 3:28.
The phrase is ubiquitous in John, but relatively rare (just four verses) in Mark. The idea that Mark's magic words inspired John is highly questionable given that. In fact we see better evidence that Matthew and the Marcionite gospels could be in view.