This is from Lester Grabbe's highly respected work:
Two biblical books claim to describe the Jews of Palestine in the Persian period; these are Ezra and Nehemiah. One of the most accepted conclusions of today is that much of the book of Nehemiah is based on Nehemiah's personal account (the so-called `Nehemiah Memorial/Memoir'). Thus, we have some indication not only of Nehemiah's deeds but even of his attitudes and (private?) thoughts. This is valuable material; on the other hand, we must recognize that it is very one-sided and reflects the entrenched opinions and biases of a strong-willed willed man. We can hardly use it as a dispassionate chronicle of events. Nehemiah's own firmly held views shape the entire narrative. The material in Ezra is quite different. In it are a number of alleged documents of the Persian administration. Although these have been widely accepted as authentic in recent English-language language commentaries, their genuineness has been strongly questioned in Continental scholarship.
-Lester L. Grabbe. An Introduction to Second Temple Judaism: History and Religion of the Jews in the Time of Nehemiah, the Maccabees, Hillel, and Jesus (Kindle Locations 448-452). Kindle Edition.
Of course, Nehemiah makes references to the Torah. Nehemiah 8 in particular describes a presentation of the "Book of the Laws of Moses".
So it seems that Gmirkin has to have some extremely coherent explanation for this. I think much of Gmirkin's work makes a lot of sense, but there are certainly weaknesses that have to be addressed.
In his latest work Gmirkin states:
Lemche pointed out that this process was dependent on a credulous reading of biblical historiographical texts of unknown date or historical value, including the stories of the introduction or discovery of new Pentateuchal legal content under Josiah (1 Kings 22–23) and Ezra (Nehemiah 8–10). While earlier biblical critics had accepted these stories as written close in time to the purported events they recounted and substantially conveying historical fact, Lemche pointed out that biblical historiographies were of highly uncertain date and contained prominent theological content that undermined their value as historical sources. Consequently they were of no direct bearing to the dating of Pentateuchal writings to which they alluded.
--Gmirkin, Russell E.. Plato’s Timaeus and the Biblical Creation Accounts (p. 14). Taylor and Francis. Kindle Edition.
But that's all all he really says about it. This is not enough. In Plato and the Creation of the Hebrew Bible, Gmirkin references Nehemiah 8, but fails to address Nehemiah's apparent reference to Exodus.
277 Levites were also given an explicit exegetical role in Nehemiah (Neh. 8.1–18). Levitical priests were brought onto the scene alongside judges and occasionally city elders wherever a homicide was committed (Deut. 21.1–9). They did not appear in a judicial capacity – judges were always mentioned separately – but instead seem to have been consulted on the proper rites to cure the pollution associated with acts of bloodshed.
--Gmirkin, Russell E.. Plato and the Creation of the Hebrew Bible (Copenhagen International Seminar) (p. 37). Taylor and Francis. Kindle Edition.
It seems to me that if Gmirkin is going to persist in this thesis he has to do a better job of addressing Nehemiah.