Three things: First I absolutely disagree with the part I highlighted. The LACK of Faith/Trust that A&E had in God is the underpinning of the entire post-Fall story! If they had trusted God, they would not have disobeyed him! Their lack of faith is what led to their disobedience just as the lack of Israel's faith in the wilderness resulted in their disobedience (Heb 3:16-19).
Secondly, I strongly disagree with your take on the sin covering. You seem to be saying that faith was not a necessary component to having their sins forgiven and covered. If so, this would be a totally unprecedented means of salvation; for the just shall live by faith! I am reluctant to buy into any theory or hypothesis that is unprecedented in scripture due to the judicial principle that is stated in the OT and NT (2Cor 13: 1), which also rightly serves as a hermeneutical principle that requires interpreters to seek the affirmation of other relevant passages. Even Noah believed God about the pending judgment of the world and his obedience to God's commands issued from that faith.
And the third reason I disagree is because God, in his infinite wisdom, provided strong evidence that Eve was a woman of faith. God's gracious provision in the animal skin coverings certainly covered her sins; but we're also supposed to believe that it covered Adam's in spite of all the negative things taught about him and the lack of any biblical evidence that he came to saving faith?