Gee Doug, I think you're opening a can of worms, (sorry, I meant snakes) with that post. Your concept could be correct, and I think you're quite correct in attempting to locate your mind in the culture of the authors of the Genesis 2 document. But that's where a big problem jumps up and bites us on the bum. What was the culture of the authors of Genesis 2.
Was the document written prior to 1000 BCE (just to attempt to see what cultural influences may have been at work)? Was Egypt the key cultural influence?
If the document was written before the Babylonian captivity, then Babylon was likely the main cultural influence. But Greek culture was also a likely cultural influence.
Or, because Palestine was on a key north-south trade route, and not far from a western terminus of a east to west trade route, were the inhabitants aware of many other cultures?
If you can get access to Stephen Harris' and Gloria Platzner's, Classical Mythology: Images and Insights, you may find many interesting thoughts on the subject of female divinities.
Quoting from the 5th edition, (p.29) an opinion is given that the Minoan and other Aegean Island cultures worshipped the "Divine Woman.' and their Ch. 5 goes on to examine the Divine woman in Greek Mythology. In the earliest information we have for that culture, the primordial goddess is Gaea. In Egypt its Isis. Serpents also have an almost universal role in folk religion, sometimes associated with a female divinity, like this snake goddess from Knossos:
And on p. 152, there's this reproduction of an image on 5th.C. BCE Athenian vase, imagining Heracles in the Garden of the Hesperides.

Heracles is resting after his journey to the land of the setting sun, where the Greek version of Gaea's 'Tree of Life' grows (and, you note, that tree has a serpent guardian). Heracles charmed the Hesperides - the nymphs who also guard the golden apples that grow on the tree, into giving him one of the golden apples (that gave immortality)..
I'd like to write more - but I'm snowed under at the moment. So thanks for posting your thoughts.