@swamidass, have you interacted with the view that “all the living” (Gen 3:20) is limited to “seed of the woman” in 3:15 (= humans of faith) in distinction to the (also human but non-believing) “seed of the serpent”? I’m sorry if I missed or forgotten this in your writings or PS posts.
This reading focuses on the special use of “life” (which is what “Eve” means) in the Eden narrative, particularly the Tree of Life that promised everlasting life in God’s presence. Since its counter “death”–result of eating the other Tree–could easily be interpreted as separation from God’s presence, it’s not a leap to consider “life” in the same manner. And the toledot of Gen 2:4-4:26 ends with reestablishment of communion with God through Seth (the antithesis of Cain, a seed of the serpent).