To all,
To maybe help steer this thread back toward the OP's intention, what Arachnophilia is saying here is, IMO, not only spot on, but his efforts to differentiate between the terms Jew & Israel also go to the heart of the premise.
It must be remembered that following the destruction and dispersal of the northern kingdom, the regnal succession of the southern kingdom of Judah was Manasseh (who "did evil in the sight of YHWH" - II Kgs. 21:2), then a very brief (c. 2 yrs.) reign by Amon, and then the first YHWH fearing king of Judah (after the destruction of the northern kingdom), Josiah, (who "did right in the sight of YHWH" - II Kgs. 22:2).
It was, then, only with the advent of the YHWH-fearing king Josiah that there would have been serious consideration as to
why the northern kingdom of Israel was destroyed in apparent conflict with the promises that had been given to the Israelites by YHWH himself.
Thus, what Arachnophilia is saying, and I agree with, is that it is suspiciously convenient that Josiah would be provided with an alleged ancient writing of Moses which tended to explain the matter precisely in condemning the worship practices of the northern kingdom (and also those which Judah had reverted to under the reign of Manasseh).
IOW, this (allegedly ancient & authoritative) document provided Josiah with precisely the foundational authority he would have wanted to both explain the demise of the northern kingdom and to implement the Yahwistic reforms he favored.
And further still, it is suspicious in the extreme that the Israelites would have formerly managed to lose and forget about one of the five books purportedly penned by Moses.
While, as Angel says, absolute proof of the matter will likely never be obtained, the overall implication seems clear enough. The original book of Deuteronomy was probably penned in the time of Josiah (c. 640 - 609 B.C.) as a means of providing Josiah with a specific authoritative foundation for his agenda.
JMHO,
Amlodhi