[The Squatter of Amon Rûdh]

Returning to the original question, the most complete discussions of Thorin's years of exile are in HME XII and UT. Forgive the long quotations: brevity will have to cede its place to completeness.

[A discussion of Thorin and Thráin's parts in the Battle of Nanduhirion precedes this passage.]

Thus [Thorin] got his name, or also because in memory of this he bore ever after at his back a shield made of oak wood without colour or device, and vowed to do so until he was hailed again as king.

When Thráin went away Thorin was 95, a great dwarf of proud bearing and full manhood. Maybe because rid of the Ring, Thorin long remained in Ered Luin, labouring and journeying and gathering such wealth as he could, until his people had fair houses in the hills and were not [? ill content], though in their songs they spoke ever of the Lonely Mountain and the wealth and bliss of the Great Hall and the light of the Arkenstone. But the years lengthened, and the embers of his heart began to grow hot as Thorin brooded on the wrongs of his house and people. Remembering too that Thrór had lain upon him the vengeance due to Smaug.

But Erebor was far away and his people only few; and he had little hope that Dáin Ironfoot would help in any attempt upon the dragon. For Thorin thought ever after the manner of his kingly forefathers, counting forces and weapons and the chances of war, as his hammer fell on the red iron in his forge.

The Peoples of Middle-Earth (HME XII), p.281

Typescript B of the early version of this tale as given in UT follows essentially the same story.

So Thorin Oakenshield became the Heir of Durin, but an heir without hope. At the sack of Erebor he had been too young to bear arms, but at Azanulbizar he had fought in the van of the assault; and when Thráin was lost he was ninety-five, a great Dwarf of proud bearing. He had no Ring, and (for that reason maybe) he seemed content to remain in Eriador. There he laboured long, and gained such wealth as he could; and his people were increased by many of the wandering folk of Durin that heard of his dwelling and came to him. Now they had fair halls in the mountains, and store of goods, and their days did not seem so hard, though in their songs they spoke ever of the Lonely Mountain far away, and the treasure and bliss of the Great Hall in the light of the Arkenstone.

The years lengthened. The embers in the heart of Thorin grew hot again, as he brooded on the wrongs of his House and of the vengeance upon the Dragon that was bequeathed to him. He thought of weapons and armies and alliances, as his great hammer rang in the forge; but the armies were dispersed and the alliances were broken and the axes of his people were few; and a great anger without hope burned him, as he smote the red iron on the anvil.

UT p.328

It's fairly obvious, even had we not Christopher Tolkien's word for it, that these passages are quite closely related. Indeed, the second is a reworded and condensed version of the first that changes no significant detail. The main point appears to be that the recovery of Erebor remains Thorin's chief concern. He takes the extraordinary step of displaying no emblem on his shield until he can recover his grandfather's kingdom; he broods on a desire to recover it by open war, but we are reminded that his people are too few and his alliances too unreliable for this to be possible. Gandalf even reminds him elsewhere in The Quest of Erebor that an army of Dwarves would have to face worse enemies than Smaug before they reached Erebor, even if such a force could be gathered at all.

It seems, then, that the Ered Luin and, indeed Eriador in general, are simply temporary homes to Thorin; convenient places to build up his wealth and following until an assault on Smaug can be mounted. To declare himself king of the Blue Mountains would in a way be an admission that he had given up the idea of reclaiming the Lonely Mountain. It seems fairly clear to me that he is uninterested in any other title, and no doubt bound up with this is the theme of the duty of vengeance that Tolkien stresses so forcefully. Thorin has an hereditary blood feud with Smaug, which is a more serious obligation even than reclaiming the kingdom of his ancestors. To take for himself any other lordship would be at best a distraction from his chief purpose.

Originally Posted by Inziladun

And when I think about it, was it really beyond the powers of a large force of Dwarves, say the size of the army at the Battle of Nanduhirion, to have destroyed one Balrog? After all, one Elf accomplished just that twice in Gondolin.

I think we need to be very careful when comparing the old Fall of Gondolin material with LR. Tolkien's conception of the individual strength of the Balrogs changed a great deal in the twenty years or so that separate them. Regardless of the possibility of killing Durin's bane, however, there are at least two reasons why the survivors of Nanduhirion would not have faced him.

The first reason is one of motive. As the unnamed survivors themselves declare: "We fought this war for vengeance, and vengeance we have taken. But it is not sweet. If this is victory, then our hands are too small to hold it." [1] The Dwarves at Nanduhirion all had homes to go to; they were not in a position to undertake a long occupation of Moria. It was more than they signed up to do.

Hinted at in these words is the second reason: the battle of Azanulbizar was characterised by heavy losses on both sides. It's likely that the Dwarven survivors were too few and too exhausted to face something like a Balrog, even had they wanted to take back Moria.

As regards the succession of Durin, Dáin is not only the most obvious, but possibly the only heir. He is the eldest remaining member of the senior line of descent, and he has an army at his back. Given the information available I can't think of someone better qualified, and Dwarves are nothing if not practical.

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[1] LR Appendix A, p.1049