What different ways to flesh out Ozai's character do you think could have been?
One of mine is this: Iroh is Ursa's brother, reasons for that is, Sozin and Azulon don't exist and it was Ozai who's been waging his war, wiping out nearly all airbenders, waterbenders and dragons the whole 100 years and the comet is renamed Ozai's comet. How this happened could go along the lines of Roku telling him about how Kyoshi lived over 230 years, and Ozai learns this trick as he plans for world dominance.
Both ideas contain a book 4: air, with the former having Ozai's comet arrive in the end of fall instead of summer. Both of them also give a much clear reason why Ozai's a primary threat and why only the avatar is supposed to stop him.
Well, one way that the writers could have fleshed out Ozai's character would have been to show more of him throughout book 3. This man was the big bad of the show, he should've had more episodes than just 3, or however many it was. Some scenes with him and Iroh, either in flashbacks or just Ozai going to see Iroh in prison would have been nice. We know next to nothing about Ozai's relationship with his brother, so some scenes with just the two of them interacting would have been very much appreciated.
Some scenes with him and Ursa would have been nice too. Disregarding the comics, in the show the relationship between these two seemed to have started out just fine, but then it began to sour thanks to Ozai being a power hungry person. Showing scenes from the early part of they're marriage before Zuko and Azula was born would have been really good. Based on that scene by the fountain after Ursa was banished, I do believe that Ozai cared about her to a certain extent. So seeing some scenes showing this would have been a good way to add something to his character, so that way he could be more than just the main villain who sits on his throne all day.