Rome had nothing to do with Jesus saying I AM. As in Exodus God was revealing Himself to man. Sorry you missed that. I AM is God showing Himself to be 100% self sufficient needing nothing from anyone or anything.Holy and eternal not sharing His Glory with another as He Himself said.Actually he was just saying I AM.
Jesus was likely saying I am the Messiah as he did when he used the same words in John 4:26
Jesus is not referring to the burning bush and there is no indication that he is. If he saying he was God, he would say before creation - not before Abraham.
Nope. You are ignoring the simplest explanations and forcing an Imperial Roman belief onto the Bible.