I finished Thomas Thompson's Historicity of the Patriarchal Narratives.
On page 325, Thompson defends the first millennium B.C.E Israelite Period as the historical setting for the composition of the stories about the patriarchs. At the earliest, Thompson dates the stories to the Iron Age. Thompson talks about anachronisms in the stories: integral elements that do not fit the time period that the stories purport to depict, namely, the early second millennium B.C.E. Surprisingly, Thompson not once in this book mentions the camels in the patriarchal narratives as anachronisms! But here are some anachronisms that he does mention:
"The tradition about Terah setting out with his family from Ur of the Chaldees for the land of Canaan, the genealogical tree of Abraham in Gen 11, the genealogy of Nahor the brother of Abraham, the tradition that Lot is the father of the Ammonites and the Moabites and his settlement to the east of Abraham the father of the Israelites, and the Jacob-Laban traditions, all bring the patriarchs inescapably close to the Arameans---those of Transjordan who were not there before the end of the Late Bronze Age in the twelfth century, the Arameans of North Mesopotamia who can probably be dated there post twelfth century, and certainly post-fourteenth century, and the Arameans of South Mesopotamia, the Chaldaeans, who were not there before the beginning of the tenth century. Similarly, the tradition which connects Esau with Edom can hardly antedate the beginning of the Iron Age, and the disinheritance of Ishmael is in its origin bound up with the conflict between Israel and the Ishmaelites. The identification with Jacob with Israel and the inheritance of his twelve sons presupposes the existence of Israel as a political and geographical entity, and the promise to Abraham presupposes the existence of the political boundaries of the Davidic kingdom. The story of the conquest of Shechem presupposes the possession of Shechem by the Israelites for a considerably period of time...
"...The reference to the Philistines in the patriarch's conflict over water rights can only arbitrarily be excluded from the story; and specifically because we do not have other evidence for the Philistines in this region, the reference appears to be original to our story...On the basis of the extensive archaeological study of Palestine, we can now say with some confidence that only during the Iron Age are all the cities of Palestine that are mentioned in the patriarchal narratives and which can be located with some certainty known and occupied. The geographical picture we get from the Genesis stories is that of Iron Age Palestine. I refer specifically to such sites as Bethel, Ai, and Beersheba."
We can see in the first quote that the narratives tie the patriarchs to particular people-groups: the Arameans, the Edomites, etc. Why? On page 298, Thompson states: "The patriarchs, and especially Abraham, are the means by which the biblical tradition has expressed Israel's political, sociological and geographical ties with the world surrounding it...Understandably, the stories often are aetiological in intent and are used to explain the historiographical relationship between the eponymous ancestor or hero and the tribe, village, or region bearing his name."
I wish Thompson had gone into more detail about why the patriarchal narratives present Abraham as an Aramean, or why Abraham is the ancestor of the Edomites in the narrative. Aram and Edom were not particularly on friendly terms with Israel, at least in biblical stories. So why did the patriarchal stories portray Israel as related to them, in some sense? Thompson does say that the agreement between Jacob and Laban was an etiology for a border, and that makes sense. But I feel that I don't know a whole lot about why the Israelites made the specific historiographic moves that they did in the patriarchal narratives---at least not from Thompson's book. But the closest explanation that I came across (that I remember from my reading, that is) was on page 302, where Thompson says that there are sociological grounds for Israel being "attached to the tribal elements in their cultural milieu (the Arameans, Moabites, Ammonites, Edomites, and Ishmaelites)". Maybe that explains why the Israelites considered themselves relatives of these people-groups: they all were alike in having a tribal background.