I agree with your belief that the Bible does not speak of inheriting a "sin nature" from Adam.
If you wrote your own version of the Bible, how would you translate Romans 5:12? Or, can you explain how death "spread" to all men, since it's our own personal sin that brings death? How can death be "spread"?
Another common belief, perhaps one that you hold, is that Adam was created immortal, but lost his immortality when he sinned. I am not sure if I can agree with this, for if Adam had immortality, there would have been no need for the Tree of Life.
We cannot say that death was not "in existence" before Adam sinned, since God didn't have to explain to Adam what death was. It would seem a little strange for God to threaten him with something that he had never heard of, you know? Don't get me wrong; I am not saying that anything/one had experienced death before Adam sinned.
Would it be safe to say that we do have the propensity to sin, but not because of Adam? The fact that Adam sinned while in the perfect environment, in God's presence, tells me that he was just as inclined to sin as we are. So what is really different about pre-sin Adam and us? The knowledge of good and evil? Was Satan being "honest" on that point?
"Therefore, just as through one man sin entered into the world, and death through sin, and so death spread to all men, because all sinned" (Romans 5:12).
There is no reason to write a new version of the Bible. There is a need to understand what the Bible says. Sin entered the world through one man, Adam. Yes, technically it was Eve who first sinned, but Adam is held responsible as the head of his family. Adam completed what Eve started. Where Eve was deceived into sinning, Adam sinned knowingly (I Timothy 2:14). With sin came death, which spread to all men (Romans 6:23). What is being talked about is spiritual death (Genesis 2:17), even though physical death also resulted from Adam’s sin (Genesis 3:19). But Paul is talking about the justification of men, so in this context we are talking about the spiritual death that results from sin. It is not because sin was inheritable but because sin is communicable – everyone sins (Ezekiel 18:20). One man created a universal problem. A simple illustration is when Eve sinned, she got Adam to sin. Clearly this wasn't a case of inheritance but encouragement.
God did not have to explain death because words have meaning and Adam was fully able to communicate from the time he was created. God did not have to explain "tree" or "middle" but Adam knew what God meant. While the command to not eat of the tree of the knowledge of good and evil was given before Eve was made, Adam clearly relayed the command to her because she talked about it with the serpent. Your argument here proves nothing.
Adam and Eve died spiritually the day they ate of the fruit. They also began the process of dying physically because they lost access to the tree of life. Their eventual death became so certain, you can say they also died physically that day.
What we can say is that when people are faced with choices, they will at times make the wrong choice. It doesn't excuse the wrong choice, only that we all make them. As Solomon pointed out, "Behold, I have found only this, that God made men upright, but they have sought out many devices" (Ecclesiastes 7:29).