You answered your own question when you said, "Actually, there is no doubt in these verses that the angel (messenger) of the LORD is simply the LORD." So what is there to "explain?"
IN GOD THE SON,
Just to clarify your view...
Are you saying the LORD who swore by himself is a PERSON?
I think you are, but I would like for you to confirm that.
Genesis 22:16... And said, By myself have I sworn, saith the LORD, for because thou hast done this thing, and hast not withheld thy son, thine only son: