Why start there? You start there in order to get the answer you want. Why do you want that answer so badly?
Muslims, after all, don’t start there (in the relevant sense). They don’t claim that God was unknown before the Qur’an came along. They claim that the Qur’an is the fullest revelation from the God who was revealing himself ever since the beginning. It is therefore irrational and unjust to define the “Islamic God” solely in terms of the Qur’an.
It is far more accurate, as well as more charitable, to say that Muslims falsely believe that God revealed the Qur’an than to say that they falsely believe their god (who revealed the Qur’an) to be the true God.
Right, but that’s not a very reasonable way to look at it for the reasons I gave above.
We need to keep coming back to the parallel with the Jews, little as folks on your side of the debate want to do so

. We don’t, as Christians, claim that the true God was utterly unknown before Jesus was born. That’s Marcionism, even leaving aside natural revelation. We claim that He wasn’t fully known. It would be unreasonable for a Jew to dismiss our identification of our God with the God of Abraham and the creator of the universe and say, “Christians worship a false god who is the Father of Jesus.” Rather, it would be appropriate for them to say (as they do, in my experience, say), “Christians mistakenly believe that the one God, the God of Israel, is Triune and sent His Son Jesus into the world to save us.”
Part of the problem here, first of all, is that phrases like “follow Christ” and “know God” have connotations referring to someone’s spiritual condition. A person who holds the beliefs you describe isn’t following Christ’s footsteps or Christ’s true teachings. But if such a person believes that the historical Jesus of Nazareth, who is also the Son of God, taught these things, then it is more accurate to say that such a person falsely ascribes these things to Jesus than that such a person isn’t talking about Jesus at all.
Now I think that your equation of Islam to Nazism is nonsense. I think there’s a lot more in common between Islam and Christianity than that from an ethical and spiritual point of view, and that most of the stuff people hold against Islam can be found in Christianity and/or the Bible (though arguably with some safeguards that don’t exist in Islam). But that isn’t the point here. Even if your analogy were accurate and not the offensive travesty it is, your argument would fail.
Edwin