As for the Deuteronomistic History (DH or DTRH), Bandstra mentions as follows,
The DH tells us that Israel prospered as a nation when the people, and especially its leadership, adhered to the terms of the covenant that Yhwh had made with the people at Mount Sinai. If the nation was faithful, they experienced prosperity. If the nation ran into difficulty, it was because they had neglected the service of its God. The consequences of history are laid out explicitly in the blessings and curses of the Torah, most clearly in Deuteronomy 27–28. A consistent pattern was seen to work out in history. If the people sinned, God sent punishment. If the people then repented, God sent deliverance. If the people got in trouble, God was always there to help but only if they reaffirmed their covenant commitment. Israel at times experienced God’s favor and at other times his wrath. But they were never disowned. This historical cycle is called the Deuteronomic theme and can be summarized by four arc of cycle: sin, punishment, repentance, and deliverance. (p192)
Some passages of the Hebrew Bible, which are summarized as follows, exemplify this perspective of DTRH mentioned by Bandstra in the cited passage above.
In Deuteronomy 28:1-68, which Dr. Lester describes Moses’ farewell or dying speech (in his lecture “Deuteronomy & DTRH B”), Moses presents blessings and curses that Israel shall have according to their obedience/ disobedience to God. First, Moses addresses that with Israel’s obedience to the Lord, constant observance of the Lord’s commandments, and loyalty to the covenant, all the blessings shall come upon their entire lives with their well-being and exaltation, which is repeatedly mentioned in the form of conditionality (If…if…) at 28:1, 2, 9, 13, 14. And next, Moses also affirms that Israel’s disobedience to the Lord, breach of covenant shall bring all the curses to their entire lives with all kinds of affliction and disaster that they have never experienced in their lives including an assault and a siege by an imperious nation like Assyria and Babylonia (28:49-50) or an exile to the domineering nation (28:36, which might suggest Babylonian exile) till they are totally destroyed. For the curses, Moses starts with a conditionality (if…) at 28:15 and then uses “because…” at 28: 20, 45, 47, to describe what brings the curses to them. And finally, the author reaffirms that even their lazy observance of God’s law shall bring them unbearable maladies and disaster till they are destroyed. In short, this passage presents the perspective of DTRH regarding blessings and curses that Israel shall have based on their faithfulness to God and his covenant.
In Joshua 23:1-16, which presents Joshua’s farewell address (The Harper Collins Study Bible, p343), Joshua affirms that God has kept his promises for Israel’s getting into the Promised Land by destroying the enemies of Israel on the way to the land. However, he continues, if Israel is tempted by the survivors of the enemy nations, serves other gods, and breaks the covenant of God, God will destroy Israel to perish from the Promised Land. This passage also emphasizes the relationship between Israel’s faithfulness to God and his covenant and the events of social and political history.
In 1 Samuel 12:1-25, which also presents Samuel’s farewell address to turn the responsibility for leading Israel over to the king Saul (The Harper Collins Study Bible, p405), Samuel asserts that the king (Saul) chosen by Israel and divinely granted by God for their request will not rescue them as God has done for them in the history and lets them realize that their request for a king to reign over them is a sin against God, who himself is the king of Israel, by demonstrating his special ability as a prophet of calling on God (12:18). He also affirms that both the king and Israel should obey and serve God faithfully with all their hearts and observe the covenant in order for them to be well. If not, both the king and the people of Israel shall be destroyed by God. Thus, this passage also reflects the perspective of DTRH and implies the close relationship between Israel’s faithfulness to God and his covenant and the events of social and political history.
In 2 Kings 17:5-18, which describes the Israelites’ (the northern kingdom) captivity to Assyria, the writer presents his Deuteronomistic point of view (The Harper Collins Study Bible p545) that all the disasters the Israelites had in the Assyrian captivity occurred because of the king and the people of Israel’s sin against God, that is, to worship other gods, disobey the commandments, and keep committing sins not to listen to the prophets’ warning to repent and keep the law of God. This passage clearly mentions that the Assyrian captivity of the Israelites was God’s punishment for the king and the people of Israel’s sins against God, which reflects the perspective of DTRH and implies the close relationship between srael’s faithfulness to God and his covenant and the events of social and political history.
In 2 chronicles 36:11-21, which describes the fall of Jerusalem under the reign of Zedekiah (The Harper Collins Study Bible p645), the writer describes the unfaithfulness of Zedekiah and the leading priests and the people who desecrated the Temple and despised God’s words proclaimed by the prophets, which he explains roused God’s wrath to result in the Babylonian exile. However, at the end, the writer adds that this is also fulfillment of God’s word proclaimed by Jeremiah. This passage also clearly mentions that the Babylonian exile was God’s punishment for the king Zedekiah and the leading priests and the people’s sins against God, which is the perspective of DTRH and also implies the close relationship between Israel’s faithfulness to God and his covenant and the events of social and political history.
As we can see in the summary of each passage, the claims of the passages appear to reflect the perspective of DTRH implying the close relationship between Israel’s faithfulness to God and his covenant and the events of social and political history. The question is “How can I assess the credibility of the positions of DTRH in the passages above?”
According to Bandstra, even though the Former Prophets may be classified ‘history’, the writers of the Former Prophets (Joshua, Judges, 1 and 2 Samuel, 1 and 2 Kings) who were supposed to be DTRH and believers in Yhwh with a conviction that Yhwh was active in Israel’s history, believed that the historical events were accounted for by divine causality in addition to human power politics and economic factors (p189). In addition, Bandstra mentions that the Jewish community’s including the Former Prophets into the section titled “the Prophets” implies that the intent of the Former Prophets was not only to record historical events but also to testify the work of Yhwh in the human history (p190). Thus, according to Bandstra, the DTRH’s writing the Former Prophets could be considered as a prophetic activity of writing history from a transcendent perspective.
Stanley also suggests that in the historical setting of Babylonian exile, DTRH’s perspective to see the history of Israel regarding the relationship between Israel’s faithfulness to God and his covenant and the events of social and political history offered two important benefits as follows.
First, it enabled the followers of Yhwh to hold on to their faith including their belief in Israel’s special covenant relationship with Yhwh, despite the painful events of their recent past. By describing Yhwh’s active involvement in his people’s history, the story suggested to the readers that their present circumstances also had meaning and purpose. Second, the narrative implied a course of action for the future. If Yhwh had brought them to this point because they and their ancestors had been unfaithful to him, then the exiles should make a serious effort to discover what Yhwh wanted form them in the present and commit themselves to serving him alone. (p252)
Like Bandstra, Stanley also claims that the goal of DTRH was not only to record events in the past, but to convince the Israelites to accept their beliefs and pertain to the fundamentally conservative vision for maintaining their identity in the midst of a foreign culture and living by the law of Yhwh to keep away from Babylonian influences with repentance of their sin against Yhwh and anticipation of the day of Yhwh’s deliverance. (p252)
Claude Mariottini  considers DTRH as an example of historiography, which he defines as “the presentation of history based on the examination, evaluation, and selection of past historical events in order to communicate a message to a specific audience.” According to Mariottini, DTRH is a historiography in that it is a prophetic interpretation of Israel’s life from their enterance to Canaan in the days of Joshua till the fall of Jerusalem in 587 BCE and the purpose of this history is to show that the Babylonian exile was a result of Israel’s violation of the commandments of the covenant. He also suggests, as another feature of historiography, DTRH’s use of only the materials relevant to their purpose and those proving their thesis among several written resources, which implies that there should be historical materials that were not coherent with the perspective of DTRH. Finally, Mariottini asserts that DTRH had a message to communicate to their audience, which he claims reflects the perspective of DTRH to see history from “prophetic eyes, the eyes of faith,” “to penetrate the meaning of events and explore their religious significance.”
With these characteristics of DTRH as a historiography, Mariottini affirms that the Book of Deuteronomy provides DTRH with the theological and ideological foundation for the proper understanding of the history of Israel; Israel’s rejection of Yhwh in their violation of the covenant, that is, their worshipping the gods of Canaan and oppressing members of the community, had brought the nation to its tragic end.
All this information that I found in the course materials provides me with some clues to assess the credibility of the perspective of DTRH by answering the questions provided by Dr. Lester as follows.
Do you find these claims coherent with other biblical witness?
Considering the DTRH’s characteristics as a historiography presented by Mariottini, I think these claims of DTRH should not be totally coherent with other biblical witness; DTRH used only the materials relevant to their purpose and those proving their thesis among the resources, which implies there would be materials of biblical witness that are not coherent with the perspective of DTRH. However, among the Books of the Hebrew Bible, I think these claims appear to be coherent with Jeremiah’s Temple sermon in Jeremiah 7:1-15 (26:1-6) where Jeremiah admonishes the people of Judah including the king and the religious leadership who had believed in Royal theology and the Zion theology about their obligations of observing the commandments of the covenant and proclaims God’s judgment on Judah, which later would be understood by the Jewish to be fulfilled by God in their Babylonian exile.
Are they intelligible in light of the way we understand the world today?
I think the answer to this question would be different depending on how we understand the world today. As a Christian, I understand the world today as a way that is somewhat similar to the perspective of DTRH; I understand the world today meaningful as it is on God’s plan for us humanity with diverse race, gender, ethnicity, and culture, etc., and other creatures, even with its ugliness filled with lots of violence, social injustice, and sins against God. However, I don’t think all the human histories are the results of our obedience or disobedience to God and his covenant as DTRH claims. Instead, I think, the events of social and political history of humanity might be the results of the sins we humanity have committed against God (similar to DTRH), not the punishment of God himself (different from DTRH). With my faith in loving and merciful God who sent His only Son, Jesus Christ, for the salvation of us, I think the claims of DTRH in the passages are not intelligible for the Christians like me in the world today. For the non-Christians today, the claims also might not be intelligible because they do not believe in God and the claims of DTRH does not make any sense for those who do not believe in the existence of God in the world.
Are they moral? How or how not? What if they are not?
The answers to these questions would be also different depending on the answer to the question of “What does “moral” mean?” If I define it as a Christian following the first definition provided in the app of “Dictionary.com”, ” of, relating to, or concerned with the principles or rules of right conduct or the distinction between right and wrong; ethical,” the answer would be “Yes, they are moral because they are concerned with God’s rules of right conduct; “Obedience to God as the only God for us and faithful observance of his covenant will bring us blessings, and disobedience bring us curses. ”
However, for a non-Christian, the claims of DTRH are not moral with the given definition of “moral” because for a non-Christian, the rules of right conduct are given not by God, but by the social norms or obligations of the community or society. Therefore, with the given definition of “moral”, if the claims are not moral, it implies that the perspective of DTRH was not credible because their claims do not relfect God’s rules of right conduct and thereby not provide a way of repentance and anticipation of deliverance from their tragic situation.
 This includes Deuteronomy and Former Prophets that were shaped by the theological perspective of the Deuteronomist (Bandstra, p190).
 “Historiography” Dr. Claude Mariottini-Professor of Old Testament https://claudemariottini.com/2010/11/15/historiography/