3. Jesus used the I AM phrase not as his name but because HE IS. Are you sure that when Jesus used the I AM phrase the Jews always interpret that usage as Jesus claiming to be divine? You have only one time that the Jews complained when Jesus used the I AM. It was when he claimed he was older or as old as Abraham. Don’t you think that is why the Jews tried to stone him, and not because he used the I AM phrase as a name but because HE IS?
The Jews didn’t want to stone him just because he said I AM did they? Everyone can say I AM because they exist. So it depends on the context in which the words are used.
“Before Abraham was, I am.”
I think this is a claim to deity because God has always known Abraham. Even before he existed as a real human being. Even at this point Jesus is existing as the Son before Abraham exists in any form, even before he exists in the mind of God. He thus claims to exist prior to all things, as God. The inference is that Jesus can point to any historical event or person and say “before this\he\she was, I AM”. He chose Abraham because the Jews were speaking about him. He could have chosen anyone else. He exists outside time. Abraham passes through past, present and future in his changing existence. Jesus as divine, does not. He has eternally existed before all things.