Thanks for the thoughtful response.
I do indeed see the story as a Fall, but not the Fall of humans, rather the Fall of souls into the material world, thus becoming human. That resolves the free will issue, because souls in the spiritual realm are conscious, therefore could choose to disobey 'God' (although that would seem to be a metaphor of some kind). They would make that choice presumably because the material world appeared attractive, perhaps the beauty of nature. The Catholic Church seems to think that it had a lot to do with the pleasures of sex, which they associate with Original Sin.
The story is therefore about the birth of humanity, i.e. souls arriving in the material world, but not about the emergence of consciousness out of unconsciousness in the sense that you suggested.
As you say, at each new incarnation we forget just about everything at birth and have to start as if from scratch once again, although we seem to benefit unconsciously from previous incarnations, and are affected by them if the law of karma is correct.
Your psychological perspective does make good sense, but only if we assume it refers to humans according to conventional evolutionary theory.
Much more to follow in the series to come. Keep in touch.