[Findegil]

DF-SL-01.4, DF-SL-01.5 & DF-SL-05: I agree that the placement of DF-SL-05 does fit Appendix A but not so much our setting. I would therefore propose the following changes:

From the sack and the burning many of Thrór's kin escaped; and last of all from the halls by a secret door came Thrór himself and his son Thráin II. They went away south with their family DF-SL-01.4{[Footnote to the text: Among whom were the children of Thráin II: Thorin (Oakenshield), Frerin, and Dís. Thorin was then a youngster in the reckoning of the Dwarves. It was afterwards learned that more of the Folk under the Mountain had escaped than was at first hoped; but most went to the Iron Hills.]} into long and homeless wandering. With them went also a small company of their kinsmen and faithful followers. DF-SL-01.5<LotR, Appendix A, Footnote 44 Among whom were the children of Thráin II: Thorin (Oakenshield), Frerin, and Dís. Thorin was then a youngster in the reckoning of the Dwarves. It was afterwards learned that more of the Folk under the Mountain had escaped than was at first hoped; but most went to the Iron Hills.>DF-SL-05b<Appendix A
Dís was the daughter of Thráin II. She is the only dwarf-woman named in these histories. It was said by Gimli that there are few dwarf-women, probably no more than a third of the whole people. They seldom walk abroad except at great need, They are in voice and appearance, and in garb if they must go on a journey, so like to the dwarf-men that the eyes and ears of other peoples cannot tell them apart. This has given rise to the foolish opinion among Men that there are no dwarf-women, and that the Dwarves 'grow out of stone'.
It is because of the fewness of women among them that the kind of the Dwarves increases slowly, and is in peril when they have no secure dwellings. For Dwarves take only one wife or husband each in their lives, and are jealous, as in all matters of their rights. The number of dwarf-men that marry is actually less than one-third. For not all the women take husbands: some desire none; some desire one that they cannot get, and so will have no other. As for the men, very many also do not desire marriage, being engrossed in their crafts.>
Years afterwards Thrór, now old, poor, and desperate, …

DF-SL-02.2 to DF-SL-02.6 & DF-SL-03b: Even so the events reported in the following additions do not belong to the tale of Dúrin’s Folk, they have a close connection since they tell the aftermath of the war of the Dwarves against the Orcs and I think therefore they should be reported here.
And I think we should give a short reminder of the history of the Ring of Thráin.

… But, as Thrór had said, the Ring needed gold to breed gold, and of that or any other precious metal they had little or none.
DF-SL-02.2<LotR, Appendix A II In {his time}the time of King Brytta of Rohan there was war with Orcs that, driven from the North, sought refuges in the White Mountains. DF-SL-02.2<based on HoMe 12; HoE; The House of Dol Amroth /The fivteenth Lord of Dol Amroth was/ {‘}slain in battle{‘ the first has ‘Battle} with Orcs{‘}.
>When {he}King Brytta died it was thought that they had all been hunted out; but it was not so.> DF-SL-02.4<LotR, Appendix A II He was called by his people Léofa, for he was loved by all; he was openhanded and a help to all the needy.> DF-SL-02.5<LotR, Appendix A II {He}His son Walda was king only nine years. He was slain with all his companions when they were trapped by Orcs, as they rode by mountain-paths from Dunharrow.> DF-SL-02.6<LotR, Appendix A II {He}Folca, Walda’s son was a great hunter, but he vowed to chase no wild beast while there was an Orc left in Rohan. When the last orc-hold was found and destroyed, he went to hunt the great boar of Everholt in the Firien Wood. He slew the boar but died of the tusk-wounds that it gave him.
>
Of {this Ring}the Ring of Thráin something may be said here. DF-SL-03b used in Of the Rings of Power It was believed {by the Dwarves of Durin’s Folk }to be the first of the Seven that was forged; and {they say that it was }given to the King of Khazad-dûm, Durin III.{, by the Elven-smiths themselves and not by Sauron, though doubtless his evil power was on it, since he had aided in the forging of all the Seven. But the possessors of the Ring did not display it or speak of it, and they seldom surrendered it until near death, so that others did not know for certain where it was bestowed.} Some thought that it had remained in Khazad-dûm …

Respectfully
Findegil