I don't think anyone is arguing against your conclusion. However, when someone changes the last point from "Mary is the mother of God with us" to "Mary is the mother of God" that the problem starts. The Son of God has ALWAYS existed, agreed? He has ALWAYS been God, agreed? His incarnation, taking on human flesh, was not when he became God, but when God became a man. The consternation comes from referring to Mary as the Mother of God - which omits that qualifier you used, Mother of God with us (whom we know is Jesus Christ). Nevertheless, there is no escaping the fact that a "cult of Mary" and Mariolatry didn't exist until men started calling her Mother of God. That title glorifies her and was not necessary for establishing the Deity of Jesus Christ.
I agree totally. You summed it up well. God has no beginning nor end.
Second, how do we know about extinct Mary cults? We do know some ecstatic cults with women priests showed up before Ephesus. Tertullian supposedly went off the rails with them. FWIW he croaked about 200 years before Ephesus.
Third, unless you're rejecting Nicea/Constantinople, God with us is God.
Fourth, what's wrong with glorifying Mary? EXCESSIVE glorification is one thing, glorification is another.
Fifth, Chalcedon gives the title or description in what's almost a throw-away line. The dispute, as presented these days, was about the distinctness of the natures and the unity of the person. If The Divinity is kind of an add-on, then one set of propositions about Christ follows. To say that from the moment of conception there is one hypostasis with two natures, leads to another and IMHO more betterer set of propositions.
Sixth, I came on this thread to dispute the etymology, not the theology.