While I remember all the hours of studying this in Watchtower publications, the Jewish side I came to learn upon leaving the Organization seems to unwind a lot of the issue.
All branches of Judaism, including Orthodoxy, agree that the Garden of Eden narrative is mythology (an origin narrative).
The serpent is not "satan" nor a demon. Speaking animals are a Hebrewism, narrative devices for warning people, like Balaam's donkey that talks to him in Numbers 22.21-39. The talking donkey is no more "satan" than is the serpent in Genesis 3.
The issue in Genesis has to do with the Mosaic Law, since the whole thing is part of the Torah. In chapter 1, humans are made in "God's image," in chapter 2 they are given the job to work in a walled garden, much like the ones in Babylon that are owned by the rich (which usually have only one entrance and guarded by armed swordsmen), and in chapter 3, they break one of the Ten Commandments by stealing from God's tree of knowledge and feel shame after they look upon one another, hiding what they look like.
According to the original Jewish view, the story was written when the Jews were in Babylonian exile and wanted to go back to the Promised Land.
Like Chapter 1 of Genesis stated, they believed it was God's purpose for them to observe all the laws of Moses, especially the Sabbath (which is why you see God himself resting on the Sabbath--why would a deity need to rest, unless the story is trying to teach something about the Mosaic Law to Jewish readers). Being made in God's image, the Jews believed they were supposed to do the same, but failed to do so as Ezekiel repeatedly points out as the reason for the exile in Ezekiel ch. 20.
The Jews were not monotheists before the exile and worshiped a multitude of gods. Even when they tried to worship the God of Abraham, they would do this in the way they wanted to, not the way the Law of Moses directed or the way the prophets taught them. After the exile occurred, they believed that God had exiled them from his "garden" much the way a rich Babylonian would a gardener for stealing.
In the story, the first parents of the Jews, Adam and Eve (who some Jews believe are historical) were placed in the myth to act as the caretakers of the Garden of Eden. They hear God's instruction to not eat from his tree of Knowledge of Good and Evil, but believe it has some power to make them like Him.
The truth is, Adam and Eve are already in God's image. But they do not believe this. They want to decide for themselves how they come to be in God's image and think that the fruit of the tree will give them what they need to do this.
It doesn't. In fact, all that happens is that they become thieves. In the attempt they become to despise one another for what they've done and hate who they are and decide that they are "naked," when in reality they were fine just the way God made them.
The story is not about how sin came into the world but laments that sin is part of the Jewish history and their failure to live up to the covenant. They lost their land. They believed, at that time in history, that God was behind the exile.
So this story was the way they explained it in relation to the need to observe the Mosaic Law and why they, at that time, believed it was important to keep it. The narrative was not intended to be read out of reference to the Torah.
Of course, the Christian take changed the view with the Pauline narrative in his letter to the Romans. And the introduction of Satan the Devil heavily personified in the New Testament wiped away all Jewish views. It was St. Augustine's Confessions that brought this together into the doctrine we know as "Original Sin."
The Christian take of Original Sin would be replaced by the Issue of Sovereignty by the Adventists which has been adopted by Jehovah's Witnesses, although few in mainstream Christian religions have ever heard of it. The reason is that the "issue" pins God and Satan as equal foes or archenemies of one another, something that is impossible in mainstream Christian doctrine.