The way I see it, he would have always kidnapped Elizabeth. I'm sure on some level he always wanted a kid, and when he found himself sterile, he wasn't going to just give up on that. Especially when he found out he was dying, and needed to start searching for a successor; and who better than his own blood. Sure, he could have adopted, but when he peeked across universes to see the no-good, self-loathing, gambler scum, Booker neglecting his child, HIS CHILD. Well that would just not stand. Elizabeth was basically Comstock's daughter, and he was sure he was a better man than Booker ever was, so to him he was doing the girl a favor.
It was probably only later that he discovered what kind of successor Elizabeth would become. Maybe there was a possibility she might have escaped, or refused to succeed Comstock. Maybe she could have killed him, or herself in some universes. But in one universe, he managed to break her, using a combination of torture, suppressing her powers, and eventually choking out all hope (as we saw firsthand). This might not have been an obvious choice, but when a ruthless dictator is faced with an all powerful rebellious daughter, it's not unreasonable to think that in one of a million universes he tried the specific horrifying method that ended up working. At that point, every Columbia universe course corrected toward this path, since every Comstock could see this possible future where Elizabeth became the prophet.
As for New York in flames, that seems like a bit of a chicken or an egg situation. It was probably always in the plan to attack the US. They forced Columbia to stand down after the Boxer rebellion; an act that infuriated Comstock so much that he seceded from the union. Beyond that, Comstock saw the US government as weak, and as enabling the very worst sort of people. But they were still a world power, while Comstock controlled a floating city, and the most advanced technology the world has ever seen. A conflict was inevitable, and frankly the fact that it took as long as it did is surprising. No doubt part of the objective in training his successor would have always involved attacking his enemies, but when he saw how gloriously her assault on New York would have gone, he probably tweaked his plans a bit to work towards that specific chain of events.