I believe that God is the greatest conceivable being, and I also came to believe
Stephen is right. We should distinguish the Design Argument from the Ontological Argument. Your question concerns neither. Your question is about the Problem of Evil, so called. How can a being who is all-good, all-powerful and all-knowing allow evil to exist? The simplest way to solve this problem is to deny one of these three propositions, and it is perfectly acceptable to deny the second: God's power is limited. This approach is taken by process theologians, who say that God is developing. For the typical process theologian, as for the Mormon, God cannot break the laws of nature, for example. The trouble with this solution is not that it does not work for the theist. The problem is that it does not work for the traditional Christian theist, and as far as I know also for the Jewish and Muslim theist. A god with limited powers is simply not recognizable as the Creator of the Universe, the Father Almighty, and so on. So the solution is logically acceptable, but theologically unacceptable.