I did this, but I reckon I should talk to you first about this, since you're really on top of the Avatar history. In short, do we have evidence that the current ruling family dates back to the very beginning? I'm getting the vague feeling that Smoke and Shadow delves more into that, but I've only skimmed that graphic novel. Can you shed some light on this? Please and thank you!
Smoke and Shadow is somewhat vague on the issue, as it states that the Fire Lords before Sozin were Zuko's ancestors, while also telling us that the current royal family (including Zuko) know very little about the Fire Lords before Sozin.
What one could read from The Shadow of Kyoshi has confirmed that the Fire Nation's noble families being descendants of the Fire Islands' warlords and has hinted that the royal family is descended from the first Fire Lord.
However! Both The Shadow of Kyoshi and other media have also stated that there were different dynasties and numerous conflicts within the Fire Nation and the royal family (In fact, TSoK's chapter 5 more or less states that Chaeryu was Zoryu's direct predecessor, yet Zoryu seems to regard Chaeryu not as close relative in the novel's epilogue).
The situation is probably similar to that of the British Royal Family: Its current dynasty, House Windsor, officially started in 1917. Yet its current head, Queen Elizabeth II, is the direct descendant to the rulers of Wessex of pre-1000. Almost all dynasties ruling Britain were, strictly speaking, part of the same family. Thus, the most likely scenario is that both Zuko as well as Zoryu are descendants of the first Fire Lord and part of the same family. However, Zoryu might not be Zuko's ancestor and be instead part of a different dynasty. Overall, the Kyoshi-era Fire Lords should be treated as "distant relatives".