If the first opinion is correct, and it seems to be so because they are stylistically similar, then it is quite possible that all the other 6 books might have been a part of Deuteronomy.
One of the most prominent Kings in the Deuteronomist History is Josiah. The son of great king David, Josiah himself became a king when he was only 8 years of age. He was very righteous in the eyes of the Lord. After Hilkiah the high priest discovers the Book of Covenant (2 Kings 22:8), Josiah get rids of the household gods, the idols, the mediums and spiritists, pagan priests and temples. He listens to the words of the Book of the Law and gets very upset: neither he nor his fathers have obeyed and acted in accordance with what's written in that Book. Josiah tears his robe. God is pleased with that. Although He's still angry, God forgives Josiah and promises that his eyes won't see all the disaster that He-God will bring on the place.
Now Josiah actually is one of the best Kings. He can be compared to Moses only in his holiness. He's great in comparison to Solomon, who messed up his relationship with God by having too many foreign wives. He's even greater than David, his father, who also had spoiled Lord's attitude towards him by messing with Uriah the Levite's wife, and later sending the soldier to death. Other kings were a complete mess.
Josiah was the one to start a reform in the government - centralization of religion. He closed all the religious centers around the country and made Jerusalem a Mecca for religious tourism. The Book of the Law thanks to him became a part of Old Testament and a part of the Deuteronomy Book. Josiah also changed the celebration of the Passover tradition. It was celebrated by Samuel in a very important religious center, Shiloh (priests of Moses - perhaps they were the actual creators of the Code of Law, as it cares about them more than of the kings; 1 Samuel 1:3-24); by David's family in Bethlehem. Deuteronomy says you have to celebrate Passover in some special, God chosen place. If God hesitates and doesn't choose one on time, then the holiday can be celebrated in various places. Josiah is also supposed to be the one who fulfilled a three hundred year old prophecy, so he's a really special one for the Jews.
In 2 Samuel 7:1-17, through Nathan the prophet, God gives David His Promise. He promises to take care of David's offspring, help him establish his kingdom, as David's kid is going to be the one who shall build a temple in the Lord's name. And the throne of his kingdom God promises to establish forever. Abijah King of Judah and the ancestor of David committed all the sins his father had done before him; he was not as concerned about God as David had been. But David had done what was right in the eyes of the Lord, so God could not break the promise given to Abijah's forefather and still made Israel a strong kingdom.
But later despite of God's promise Judah gets destroyed by the king of Babylon (and the temple built by Solomon as well). That happens because of Manasseh who sinned against God including shedding innocent blood. God simply could not forgive him for filling Israel with the blood of innocent (2 Kings 24:2-18, 25:1-26).
Almost forgot to mention Solomon's Covenant with God. Solomon has been the king of Israel for more than forty years, and he built a temple dedicated to God. God was very nice to inform Solomon though that in case he or his sons turn away from God and stop observing his commands and decrees, He shall then cut Israel off the land given by the Lord, reject the temple that has been consecrated in His name. Solomon turned out to be an OK king, not as great as David, but still fine, better than some of his descendents.
The author of the Deuteronomst History series could be Jeremiah. His father was a high priest (Hilkiah), one of the Moses' descendents (Anathoth priests), and among his friends were: Ahikam the son of Josiah's secretary and Jeremiahs own secretary Baruch, who served him as a 'typewriter'. So they were quite close to the king. I could be the king himself, but that is the version that is harder to prove. Another assumption may be, that it was Baruch himself, but it would be hard to imagine as Jeremiah only could be the source of information for him.
As the original law was destroyed in fire, Ezra had performed the duty of a final redactor. He copied the remaining stuff down and the rest he claims to have been dictated to him by the voice from the bush. He claims that God visited him and gave him inspiration to write it the way it always had been. He rewrote the Jewish tradition two centuries after the birth of Christ. It's even hard to believe it. He took all the different sources and compiled them together. He had no right to miss a single source otherwise the book could be called not real.
He put all the stories together so that the difference was not seen.
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