The problem with Logotokos, AFAIK, is that Logos, the second Person of the Trinity, cannot be "born" (i.e. APPEARED after He was not). God (Who is the Father and the Logos and the Holy Spirit) can will that the Logos will become incarnate - but the Logos had been before this will came to pass.
Christ, on the other hand, was born (=appeared as a God-Man), and He was God. His one unique Person (Hypostasis) had in itself the Logos (Who, in Himself, apart from Christ, cannot be "born"), and a man (baby) Jesus who was most certainly - directly - physically - BORN by Our Lady. In Christ there was God - so, His MOther was the Birth-Giver of God.
It all boils down, AFAIK, with how we understand Birth in the case of Christ. If we understand birth as beginning of something new - then no, the Logos cannot be "new." He is immutable, unchangeable. Can God be new? Paradoxically, yes... He may will that He will be new from the moment of Annunciation. He will now be God incarnate. A new action of God, His new (from our human vantage point) will, desire, manifestation, Theophany. But He is the same Loos nonetheless, unchangeable, immutable, with no death and no birth and no movement and no passion and no alteration.