Does Scripture actually say that eating from that Tree once grants eternal life? Or can it be that eating from that Tree extends/renews life?
It's merely described as the Tree of Life. It's properties are actually not described.
Heb 10:1 For the law having a shadow of good things to come, and not the very image of the things, can never with those sacrifices which they offered year by year continually make the comers thereunto perfect.The tree of life is like a shadow, the image of Christ. It is one of many pictures of Christ scattered through scripture, each giving us a different perspective of Christ. If you put them all together you will have a pretty good 3D picture of him.