Your post is obviously well-researched but completely disregards the bulk mine, specifically the thrid paragraph. To expand:
The current scientific theory of the age of the Earth is well supported by the geological evidence and I have no interest in disproving it. I advance the view that the story of creation has much less to do with time in terms of days and years and much more to do with the rhythm of the Earth and humans specifically. I argue that the reason we should keep Shabbat is because of the word "day" used in the Bible, regardless of whether it is used to signify "24-hour period" (which I personally do not believe, though I can't speak for others) or "stage of creation" (which I think to be much more likely and useful).
I have already studied most of the human history you've laid out. Megiddo is new to me, but Old Jericho is not. I accept it all as fact (or at least a very good approximation), but irrelevant to my observance of Shabbat AND I don't find it a compelling reason to call the book of Genesis "junk". That assessment still stems from wanting "day" in the Creation story to mean 24-hour period, when in fact, when you take a long look at the wording of the Bible, G-d does a bunch of creating, then the Bible says "and it was evening and it was morning, one day" or however many days had passed up to that. Who knows? Many G-d "paused" time while He did the creating, then made a 24-hour day pass.
The point is that it isn't useful to take the word "day" literally in the Creation story, nor do I believe that's where its true meaning lies. It's pretty obvious that the world is older than the 5770 we've calculated back from the Bible, as you've very kindly laid out. (That number comes from a bunch of Rabbis in (I believe) the Middle Ages who wanted to figure out how old the Earth was. It's not a result of our day-counting tradition.) But instead of taking this as evidence that Adam and Chava weren't the first people around, I suggest an alternative.
The year-counting Rabbis used Genesis 5 to count how many years passed between Adam and Noah, using that string of "And X begat Y. And all the days of X were so-many-and-such." However, the Bible uses in several cases the word "son" to mean "descendant" (see: G-d's promise to Abraham, the "sons" in Pslam 80, the "child" and "son" of Isaiah 9:15). It's easy to see how several generations could be left out. (And even more in the "begats" between Noah and Abraham) It's no stretch, considering that each of the men mentioned in the geneology also "begat sons and daughters" who remain nameless. The Torah clearly has no qualms about leavning names out. And so, it's very easy to reconcile the ideas of an Earth older than 6000 years old, leaving plenty of time of the nameless sons and daughters of Genesis to become Egyptian, Hassuna, Samarra etc.
You may say it's implausible and you may not believe it. Say I'm stretching it if you want, but it can't be disproven. But I'm reading through the collected adventures of Sherlock Holmes and to paraphrase him, once you've eliminated the impossible, whatever is left, no matter how unlikely, is the truth. I don't see how it's possible to stop believing that the Torah is Truth (for me. I get how other people stop believing). I don't see how it's possible to discount the mountain of evidence in favour of an old Earth. Therefore, there is some unlikely-seeming explanation that harmonizes them and I think I've found an OK one so far.
As to the flood, this really isn't the right place for that argument. (I will say that my reading of the Bible can offer no hint as to the actal date of the flood since I don't think the 5770 number is accurate.) I've avoided entering the debate threads about it specifically because I find them too crowded. I will look into those books, though. I do find the historical and geological studies of Biblical times fascinating--when the science is good, that is. I can't stand the anti-evolution pseudo-crap that gets spread around.
As for your choice of words--if you want to see junk, that's all you'll see. In your posts, you've focused mostly on combatting a hyper-rigid and closed-minded interpretation of the Bible which I don't hold. It's not the Bible that's off, it's your interpretation. When you give yourself permission to believe in it, the Bible makes it pretty easy. It was MADE for us to delve into. I guess you could call a surface reading junk, if you were into inflammatory language like that. [I find it usually just gets blood boiling and tend to stay away from expressing myself in it, even if I'm thinking it.] A surface reading really does misunderstand the message AND the purpose both.