The idea of God having a moral sense can be addressed with basic symbolism within Genesis. There are two trees in the garden of Eden, the tree of knowledge of good and evil and the tree of life. The tree of knowledge of good and evil is connected to morality. Moral laws tells us what is good behavior and what is bad/evil behavior and therefore these laws gives us knowledge of good and evil. This symbolism shows this tree is occupied by Satan, not God, which is why Adam and Eve are warned not to eat from that tree. That tree leads to death not to life. The tree of life, on the other hand, is connected to the true nature of God. There was never any taboo about this tree. However, it was cut off after the fall to avoid moral law enduring forever. The time for morality was designed to be finite, not infinite; it was nailed to the cross and ended.
In Revelations of the bible, we learn more about the tree of life. It has twelves types of fruit and its leaves are for healing the nations. This symbolism is much more God-like since it is not a one trick pony, like moral law. God has more to offer. The knowledge from the tree of life is like life itself, both adaptive and always optimizing. If you look at life in the sense of natural selection, whatever the circumstances may be, life somehow adapts and the most optimized is naturally selected. This is the nature of God. Twelve types of fruit, I would guess, would be twelves aspects of adaptive optimization via something similar to natural selection. It is creative and promotes the twelves dimensions of life to endure and improve. Jesus gave us one of the fruits which was love; love is like fertilizer for the soul. Love finds a way to live and grow. There are other fruits. Truth is another of the fruits of the tree of life.