I started John Van Seters' Abraham in History and Tradition, which I am actually rereading, since I read the book over a year ago.
I didn't get too many pages read so far, but what stood out to me in what I did read was than Van Seters said that he was not just interested in the dating of strands of the Abraham story, but also in the function of the Abraham story. I pretty much know what he considers to be its function: to provide the exiled Jews with a story about God's unconditional covenant, after Israel had violated and been punished for the conditional covenant---which said that Israel had to obey God's laws to remain in the land. What was Israel to do after failing? How could she have assurance that she was still God's people and would inhabit her land? The answer was that God made an unconditional covenant with Abraham---which was not based on Israel's merit. Or perhaps it was based on Abraham's merit, not that of Israel. Van Seters made that point in Prologue to History. I'll have to see how Van Seters' thesis plays out.
An important point is that Van Seters does not believe that the Yahwist (J) concocted the story of Abraham out of thin air, but that he used oral traditions. What function did those oral traditions play? Does Van Seters interact with this issue? I will see!