Christianity did a much better job at it, no doubt. Islam does believe that the Bible was corrupted by the evil Jews and Christians.
The Torah is clear: God is One. Over and over this is repeated, the unity of God is made clear. Not three, I'm afraid, so Jesus can't be divine, and there can be no Holy Spirit distinct from the Lord Himself. Furthermore, whatever Jesus' merits, he fails the test of Deuteronomy 18:20, thus he is no prophet either. Righteous he may have been, and his teachings of how men should behave to one another are worthy, but ultimately he is no more than the vehicle that brings the lessons of the Torah to the gentiles. That alone brings to Jesus great respect in my eyes, but not enough that I would deny the clear word of the Lord Himself, Adonai Echad.
Koran is not based on Old Testament or the New but on the Mohammad views. Muslims believe that Koran CONTAINS all teaching of the Bible and that the Bible owned by Jews or Christians is corrupted and to be avoided.
I respect your position. But I would also say that the Eastern and Western Fathers were clear in emphasizing the fundamental unity of the Trinitarian God (without falling into the trap of either docetism or polytheism).