What is a "person"? One's person is one's distinct "self", that is a distinct self aware consciousness. You are a distinct person from me because you have a distinct "self" or "self aware consciousness". Also, you are a separate "being" because you are a separate living thing in relation to me. So a "person" is a "self", one who can say "I" in relation to others.
Jesus prays to the Father as though He's another person. Jesus said, "I AND my father ARE one." The "self" (person) that prayed to the Father identifies Himself as the I AM and having been before Abraham. The same "self" or "person" that prayed to the Father also said that He possessed glory with His Father before the world was. John tells us that prior to incarnation the Son was the Word. It was the Word that was made flesh, not the Father, though John also tells us that the Word that was "with God" was also "God". This is a distinction with unity of being.
I propose that the very person of Christ is indeed a distinct divine persona that subsisted within the Father from eternity. Thus He is both distinct from God the Father (a biblical term) and at the same time existing in unity of being, from all eternity, with God the Father.
Imagine "Oneness" but from an eternal perspective that sees the person of Christ as eternal, not just a man from Bethlehem. And even IF Jesus was just a man, complete humanity (human body, soul, and spirit), He'd still be a distinct person because in relation to the Father Jesus can say, "I" with distinction. So such a theory would still have two "persons", only it would express the notion that we'd have one divine person who is in unity of being with a human person.
As long as Jesus says "I" in relation to Himself and "You", "Thou", or "Thee" in relation to the Father, He is a distinct "person". For example,
Jesus says...
"I and my father are one." ("I and")
If Jesus was the same "person" Jesus would say...
"I, the father, am one."
So rather you believe that Jesus is a distinct divine person who is one in being with the Father from eternity or that Jesus is merely a human being that was the complete humanity in which God was manifest, you have two distinct "persons". No way around it.