You are going to have to make that analysis work.
Firstly, Eve had never had a birth. And we really can’t tell what God had in mind for Eve if she had been able to stay in Eden. Do you think God really planned on having 7 billion humans in Eden? Or, is it more reasonable to think that God had no plan for exponentially increasing numbers within Eden? But let’s say he had in mind Eve giving birth to two replacement children: within the precincts of Eden, he could have put Eve to sleep just like he put Adam to sleep.
Adam and Eve would not need to live by the sweat of the brow, unless they were doing aerobic exercises just before they went to pick up some melons down by the stream.
And as for dying… the Tree of Life was designed to take care of that issue.
So all the elements of God’s “curse” on Adam and Eve came to pass because of their expulsion.