The flesh is a BASE NATURE and has nothing to do with being "born guilty" or being "born condemned" or being "born disabled from being able to yield to God," all of which the doctrine of Original Sin teaches.
I agree with your proposition that the nature of Adam did not change at the fall.
But let us go back to what God said was the problem. "If you eat of the tree of knowledge of good and evil you will die."
So Adam with knowledge would loose eternal life, communion with God and would die.
His descendants who are born into this state and knowledge would die.
We there fore inherit death from Adam, and we inherit knowledge, or self awareness.
The idea the knowledge made them self aware is mentioned by Adam and eve did not know they were naked.
Nakedness was not a problem to them until they gain knowledge.
Now the question you are not asking is what is the sin? Gaining knowledge or disobeying God? Which brought death? The knowledge or the disobedience or both?
I would suggest to you the solution to the problem of knowledge brings death because knowledge corrupts you, because without love to balance it in your heart it entices you with emotional reward apparently at no cost.
So what is Gods answer to the problem? The cross, the infinite demonstration of love, sacrifice, order, appropriateness in the face of sin and corruption. The power to overcome is to know you are loved, to a degree you cannot truly imagine. It is this you are giving up when you sin, when you take short cuts, when simple pleasures appear better than holding your own.
Now to the unsaved there is no answer to sin and destruction, for they have no acknowledgement of the creator or His heart and only can see selfish gain at the price of others loss. They will always be driven to this behaviour, and so by doing destroy themselves.