You're not wrong, Colin. In the film, Michael consolidated his power in New York by whacking the heads of four rival Mafia families, plus Moe
Green, plus Carlo. But in the novel, Michael only whacked Philip Tattaglia and Barzini, plus Carlo, on the Day He Settled All Family Business. He evidently reached an accommodation with the two surviving NY Mafia Dons (he'd dispatched Moe Green previously).
Why did the film deviate from the novel in this regard? Mainly to make for a far more dramatic conclusion through a surfeit of violence. Even so, we subsequently saw that Michael had no real peace. In a deleted scene, we hear from Neri that Fabrizio emigrated from Sicily to America "in 1956, sponsored by the Barzini Family." So even though Barzini was murdered in '55, his family apparently was intact and still making mischief against Michael. And, as we saw in GFII, the "olive oil business" that Michael had handed to Clemenza after the Great Massacre was now falling apart under Pentangeli.