On the authorship of the Deut:
On the version that Deut was written by Jeremy before the destruction of the First Temple: The "Book of Law found in the Temple" during Josiah's reign (and Helkia's rule as the achipriest) was, possibly, a collection of old texts that documented the early oral tradition and were stored in the Temple. Helkiah decided to hand the scrolls to Jeremy, his young, talented, educated and passionate son. Jeremy composed Deut using the material from the scrolls, because Duet quotes all earlier books of Moses. It is quite plausible that Deut was written by a very young person. Such an outright maximalism is hard to make up. IMHO Jeremy is (likely) the author-editor of Deut. Deut is a single book, not a compilation. מִשְׁנֵה הַתּוֹרָה - "a manuscript rewritten from another script [of Torah]". Jeremy, who came out of the temple clergy, created a work using older manuscripts and carefully extrapolated the tradition. In particular, he inserted the importance of the Temple, which was the issue contemporary to him (cult centralization by Josiah, whom Helkiah and Jeremy supported.
of course, it's just one of several possibilities that I personally like.