On Dating Mesopotamian Influence

No, this post doesn’t directly deal with the question of Mesopotamian influences on the Hebrew Bible. If you’re too disappointed, I will mention it at the end of the post.
Scholars like Martin West and more recently Burkert plus a host of others, have noted Mesopotamian influences in Homeric epic. If one thinks in terms of Near Eastern influences more generally, the modern discussion goes back to at least Hugo Grotius’ 1644 commentary on the Hebrew Bible. And of course, some ancient Greeks also saw Eastern, if not specifically, Mesopotamian influence in their culture. The history of the discussion includes the likes of Cyrus Gordon and Michael C. Astour. Walter Burkert himself devoted a different book to the general subject in 1985.
But those specifically Mesopotamian influences in Homer raise an important question of chronology. They almost had to enter the Homeric tradition before the Persian period. I know its controversial, but if one accepts Geoffrey Kirk’s assessment concerning to origin of the epics, “In short, the eighth century B.C. was exactly the period in which conditions were at their best for the production for a monumental oral epic” and that the Iliad was committed to writing in the early 7th century BCE, then trivially any Mesopotamian influence must predate the early 7th century and likely the late 8th century. And it was exactly at this time that the Ionians had some kind of military contact with the Assyrians. Assyrian texts, one a letter to Tiglath-pileser III and another an inscription of Sargon II mention the KURia-ú-na-a-a. The Sargon inscription refers to them as, KURia-ú-na-a-a ša šu-bat-sún [ina] M[URUB4 ta]m-tim, “the Ionians who live [in the mid]st of the [s]ea.” In case you are wondering, this can hardly mean Cypriots; the Assyrians word of Cyprus was Yadnana. This doesn’t necessarily mean that the transmission vector was direct or in every case (or any case) in the 8th century BCE. It doesn’t necessarily exclude, for example, Phrygian mediation. It also doesn’t mean that these early influences weren’t reinforced later or that other Mesopotamian influences didn’t enter Greek thought later. It only means that some Mesopotamian traditions had to arrive during the period of Assyrian hegemony or before.
Does this inform the timing of Mesopotamian influences on the Hebrew Bible in anyway? I think so and I think I know a couple of rather clear examples that may not in the normal list of influences but I’m not quite ready to go public with them.

Astour, Michael C., Hellenosemitica, An Ethnic and Cultural Study in West Semitic Impact on Mycenaean Greece (Leiden: Brill 1967)
Burkert, Walter, Babylon, Memphis, Persepolis: eastern contexts of Greek culture (Cambridge, MA.: Harvard University Press, 2004)
Burkert, Walter, The Orientalizing Revolution, Near Eastern Influence Revolution (Margaret Pinder and Walter Burkert trans; Cambridge, MA: Harvard University Press, 1992); originally published as Die orientalisierende Epoche in der griechischen Religion und Literatur (Heidelberg, 1985)
Gordon, Cyrus H., The Common Background of the Greek and Hebrew Civilizations (New York: Norton, 1965)
Grotius, Hugo, Annotata ad Vetus Testamentum (Amsterdam: Lutetiæ Parisiorum, 1644)
Kirk, Geoffrey Stephen, The Iliad: A Commentary: Volume 1, Books 1-4 (Cambridge: Cambridge University Press, 1985), 16.
West, Martin L., The East Face of Helicon: West Asiatic Elements in Greek Poetry and Myth (Oxford: Clarendon, 1997)