I think you've hit on it here, Juv. We can attain eternal life by keeping the law perfectly. This isn't feasible now, but it was in the garden before we had a sin nature, and before we were aware of multiple laws. For at that time we had access to the tree. Sin banished us from that source. Now Jesus Christ is our only path to eternal life, so He in essence has become our tree of life. This is very plain language for us and the ancients to understand.
But it was very astute of you to point out angels. They had a choice before them and those that chose wrong apparently found themselves with a very permanent fate. I don't know that they had access to a tree of life, themselves, or if they needed that for eternal life. But whatever means God gave them for eternal life, they lost access to it when they rebelled.
But the fact that Jesus is called the tree of life, no more allegorizing the tree in the Garden, than it does a loaf of bread. For He's called that too. He's also called living water. Does this mean water is just an illusion?
Such notions are not christ-centered reasoning, they are just bad deductive logic.