You were right when you wrote, "since Jesus was God incarnate" "she could be viewed as the Mother of God." Why not stop there? It's simply a fact. And the negative you add does not necessarily follow: she was human and gave birth to a divine Person, the Second Person of the Trinity. When a human mother gives birth to a human child, the mother preexists the child. But even you would agree that this was not a merely human child, that the prexistent Word by uniting with the human nature provided by his mother, came into a new union-existence (called the hypostatic union) but did not come into His own Existence at that point. Mary preexisted the hypostatic union, yes, because it was her body and her will (cooperating with God's eternal design) that made this union possible.
If that to which Mary gave birth was the Eternal God incarnate then it has two aspects: it is the Eternal God and it is incarnate. Mary as mother did not preexist the God aspect but did prexist the incarnate aspect becaues this is an in - carnation, something that has a beginning in time even though the Person who is here incarnated is eternal and always existed. His Incarnation did not always exist.
This illustrates the fact that most Protestant objects to veneration of Mary result from never really thinking the issues through. What you view as a telling argument against Mary as Mother of God actually underscores how real the incarnation was: If God truly became incarnate in time through a birth, then God had to have a mother in time. When we say "Mary Mother of God" we do not say Mary Eternal Mother of God but Mother of God. Of course it's a stupendous miracle and mystery that a mere woman becomes mother of the Eternal God but no more stupendous than the claim, which you Protestants share with us Catholics and Orthodox, that God the Worde truly became incarnate, in time, from a mother.
"You were right when you wrote, "since Jesus was God incarnate" "she could be viewed as the Mother of God." Why not stop there?"
Because to do so would be imprecise. Mary is not the "mother" of God the Father not is she the "mother" of God the Holy Spirit.
"This illustrates the fact that most Protestant objects to veneration of Mary result from never really thinking the issues through."
Usual tired argument. "Your just not as smart as us."