The Father and the Son both say: "It's me"

Last week, I wrote about my struggle to understand the famous phrase I am [that] I AM (Exodus 3:14), and how I was inspired to interpret this phrase as I am the one who is with you. I thought I was done withe Exodus 3:14, but I stumbled upon another famous scripture that forced me to reconsider I am [that] I AM: in both John 18:5 and Mark 6:50 ("be of good cheer, it is I"), Greek phrase ?γ? ε?μι [ego eimi] is translated to I am, which Biblical scholars have apparently made the connection to the I AM in the Exodus 3:14. But I am getting a spiritual prompting to translate both the I AM [`eh-yeh??·?er?`eh-yeh] in Exodus 3:14 and the [ego eimi] as: "It's me: your God"

I am afraid to of interpreting the scripture on my own; after all I am no biblical scholar. But after listening to Elder Bednar's talk Is it the Holy Spirit or is it me? (in which he assures that if we live righteously, these promptings will not lead us astray) I feel more confident that I have the permission to act on these spiritual promptings. Besides, my Patriarchal Blessing promised that ?"the Holy Ghost will never prompt you to do something that you cannot do".

The prompting to interpret [`eh-yeh??·?er?`eh-yeh] as It is I is significant, because it means God not only knows me intimately (well, technically Moses, but I am reading the scripture personally), but expects me to know Him intimately–as a son knows the father. Thus, written out long-hand, I re-interpret Exodus 3:13~15 like this:

[Moses] Suppose I come to the sons of Israel and say: the God of your fathers has sent me to you, and they ask: what is his name? What shall I say to them?

[God] It's me, Moses. Say to the sons of Israel: the being who says "it is me" (to me) has sent me to you. Yahweh God of your fathers, the God of Abraham, the God of Isaac, the God of Jacob has sent me to you. This is my name forever, my alias to all generations.

I am curious why my interpretation is not enumerated as one of the possibilities in Wikipedia or mainstream Christian discussion on the subject, and wonder if this is because of my Korean culture. Growing up, my mother was called by friends, family, and neighbors as "Henry's mom", and my dad was likewise called "Deborah's father". It's in the Korean culture that a commoner is informally identified by the children's name, so it doesn't feel strange to me that God would choose to identify himself as a personal God. But that part of Korean culture is going to way of the Dodo bird, and besides, I am more American than Korean, so I know how unusual it is for the almighty God to identify Himself as just "it's me". TBH, if I were God, and Moses had asked me to introduce myself, I would have said: "the creator of the Heaven and Earth, and everything in it, including YOU, you ungrateful vermin!"

And this is why I am moved by God's kindness: even though he has the power and the right to exercise prerogative over me, he holds back in order to give us the gift of agency, and so instead lowers Himself as merely our personal God and the father. And even though we don't recognize him as such at first due to the veil of mortality, he still just says "it's me" when we ask him in ignorance to identify himself. I picture an image of a concerned father looking down at his child who woke up with an amnesia: how concerned he must be for the child, and how frustrated he must be that the child does not recognize him!