I agree with your interpretation right up until you said: Adam's one known sin of eating the fruit, caused mortality (part of God's plan) and Christ's role was to redeem that mortality and convert it to immortality through his sacrifice.
I believe that God's plan was always that humans would be mortal and that is why the physical body is biologically programmed to die. With all due respect, I think it is absurd to believe that process could be reversed or that it would even be desirable to live in a physical body for all of eternity.
I believe that the death of man is merely his soul passing from one world into another, and when the soul passes from this world into the spiritual world it takes on a new form comprised of spiritual elements. Since there is nothing physical (e.g., oxygen, water, food) in the spiritual world (heaven) a physical body cannot exist there and is of no use to anyone. I also believe that Jesus is alive in heaven in a spiritual body that is immortal, not alive in a physical body.
So the immortal body is a spiritual body, not a physical body.
Back to the Tree of Life, below is a post I posted some time ago on a Christian forum.
Christians believe that the tree of life was a source of ongoing physical life, that Adam and Eve were designed to live forever, but to do so they likely needed to eat from the tree of life.
What is the Tree of Life?
“In Eden, the tree appears to have been a source of ongoing physical life. The presence of the tree of life suggests a supernatural provision of life as Adam and Eve
ate the fruit their Creator provided. Adam and Eve were designed to live forever, but to do so they likely needed to eat from the tree of life. Once they sinned, they were banned from the Garden, separated from the tree, and subject to physical death, just as they had experienced spiritual death. Since Eden, death has reigned throughout history. But on the New Earth, our access to the tree of life is forever restored. (Notice that there’s no mention of a tree of the knowledge of good and evil to test us. The redeemed have already known sin and its devastation; they will desire it no more.)” What is the Tree of Life?
Baha’is believe that the tree of life is the Word of God which bestows eternal life. This tree of life was the position of the Reality of Christ; through His manifestation it was planted and adorned with everlasting fruits. Eternal life is a quality of life, of being near to God; it is not physical life, but spiritual life. God never created the physical body to live forever. Once the physical body dies, the soul leaves the body and ascends to the spiritual world where it takes on a new form comprised of spiritual elements that exist in that realm.
It is a tree of life to all who grasp it, and whoever holds on to it is happy; its ways are ways of pleasantness, and all it paths are peace.
“The tree of life is the highest degree of the world of existence: the position of the Word of God, and the supreme Manifestation. Therefore, that position has been preserved; and, at the appearance of the most noble supreme Manifestation, it became apparent and clear. For the position of Adam, with regard to the appearance and manifestation of the divine perfections, was in the embryonic condition; the position of Christ was the condition of maturity and the age of reason; and the rising of the Greatest Luminary 4
was the condition of the perfection of the essence and of the qualities. This is why in the supreme Paradise the tree of life is the expression for the center of absolutely pure sanctity—that is to say, of the divine supreme Manifestation. From the days of Adam until the days of Christ, They spoke little of eternal life and the heavenly universal perfections. This tree of life was the position of the Reality of Christ; through His manifestation it was planted and adorned with everlasting fruits.”
Some Answered Questions, p. 124
From: 30: ADAM AND EVE