"Thus, Mary can be properly called "Theotokos" because she bore the ENTIRE GODHEAD"
No, the scripture is clear that the Father sent the Son. The Father and the Holy Spirit did not become flesh. What you are proposing is a form of modalism, somewhat like the "Jesus Only" pentecostals.
1Jo 4:10 Herein is love, not that we loved God, but that he loved us, and sent his Son [to be] the propitiation for our sins.
The Son was sent, but the entire Godhead was still present in Christ. What part of Divinity stayed "behind"? It is a mystery on exactly what happened at the Incarnation. Only the Logos became flesh, but the entire Godhead became flesh because within the Logos is the entire Godhead. Unless you believe in three Gods.
Regards