Generally in a literary-canonical approach we do not dive into questions of multiple authors but simply study the text as we have it. Usually such lines of inquiry have been laden with faulty presuppositions and with agendas to undermine the word of God as we have it (look no further than the bogus JEDP theory, which has torn apart Scripture without any benefit to the church and honest scholars today would admit that it is highly speculative and is the product of particular biases). But it is helpful for those who hold Scripture to be fully the word of God to note what lines in Deuteronomy are the product of a later human hand so that we can see what this finished product of the Spirit is teaching us today.
Aside from the additional poem and epilogue by the editor(s) [hereafter simply, ‘editor’], there are few indications of a later hand in the text. The “these words” are not only faithful to Moses but are his very words (as noted in an earlier post, the vocabulary was updated later but this does not change the meaning). And the bulk of the book has this early origin. (As fitting with what I have said above, the whole book when completed is fully the word of God even in the choice of words). But there are a few places where we see the editor’s hand.
In particular we see this in the remark “to this day” in Deut 2:22 and Deut 3:14. We already noted that this phrase points us to the editor in the second epilogue and it often does so in other places in the Torah as well. Most of the editorial comments explain geographical issues (people groups and places). These comments interrupt the flow of the passage so much that English translations usually put them in parentheses. For example Deut 3:9 and Deut 3:11 are editorial additions. In particular, verse 11 shows us the main interest of the editor — King Og was one of the Rephaim (from the size description it is obvious that Og was one of the giants). McConville explains that Canaanite giants were called Anakim [sons of Anak from the Nephilim according to Num 13:33] (Deut 1:28, 9:2), Moabite giants were called Emim (Gen 14:5, Deut 2:10-11), Ammonite giants were called Zamzummim (Deut 2:20, perhaps also Zuzim in Gen 14:5), but Rephaim was the generic title for all such giant races (cf. Deut 2:11). One only needs to read the text in English to see all of these parentheses about giants. Interestingly, the editor also made comments about giants in the book of Joshua (Josh 14:15, 15:13, 21:11 all mentioning that Arba was the father of Anak).
As an aside, I think it is unhelpful to dismiss these editorial comments as less than Scriptural or to think of them as extrapolations and interpretations in later preaching. These additions are inspired of God — they come from a later human hand — but they tell us something God wants to teach us.
So why is the editor obsessed with these giants? For one thing, this is why the previous generation (save Joshua and Caleb) were not prepared to enter the land but here we see the next generation defeating a renowned giant even before entering the land and they defeated peoples who had defeated giants. This also helps us understand as well why the people of the land were so afraid when they heard that Israel had defeated King Og. It is also worth noting that we can trace the theme of giants in Scripture to Goliath and to Satan (maybe the reason for the word choice of Rephaim in as much as other texts use the term for those living in the underworld — McConville cites Psa 88:11, Job 26:5, Isa 26:14 for this meaning but admits that we do not currently know if the two meanings of Rephaim are related). Are there any other reasons you think the editor would be so interested in giants? Aside from what I said above, perhaps they help the text preach to a new generation that is facing metaphorical giants? One of the major concerns of Deuteronomy, shared by the faithful editor, is the preaching of Torah to a new generation. So there may be something to this.