[Kuruharan]

Did his desire for vengeance on Smaug, one which apparently also occupied his thoughts while he was "engrossed in his crafts" preclude him from having an heir? Was he too focused on his stolen birthright to take an interest in marriage?

These are both likely to be the case.

Fíli was born in 2859, when Thorin was 113 years old.

I'm at work right now and without access to my books so I can't look up if Thorin had settled in the Blue Mountains during his prime marrying age. If they were still wandering to some degree during that time, that probably also played a role in Thorin not marrying.

If the odds of Dwarves reproducing are as low as they are purported to be (only one-third of the population women, and neither all women nor all men willing to marry), would the birth of a nephew have been fortuitous for a Dwarf King like Thorin, brooding on the wrongs done to his House?

Undoubtedly so. The birth of a nephew would probably be viewed as fortuitous even in the best of times.

One thing about Tolkien's conception of the dwarves that I have always found...not entirely well thought out, is their lackadaisical attitude toward their own continued existence. If females are rare, and consequently marriage and child raising as well, one would think that marriage and family would be something culturally valued and encouraged rather than being seemingly viewed as incidental.