Do read the acta of the Third Ecumenical Council. They are available on line in the Eerdmans translation.
'Christotokos' was the title Nestorius insisted on, and it was precisely because the title introduced a distinction between 'the one from the Virgin' and the Divine Logos that the Church has inisted on the title Theotokos as a guard of sound Christology.
I will read them. But you see the problems the emphasis on Mary causes.
Why not just call her mother of Jesus and then develop the Christology from the person of Christ rather than stemming from Mary?
Mother of the incarnate Christ I think solves the issue since it does show his preexistence as God without negating the fact that he was God when Mary gave birth to him.