All those Families seemed to be playing the fence (especially Bruno and Zerilli) during this situation. Chicago was kicking up alittle dust about Vegas and Arizona particularly orchestrating some bombings in Tuscon. But they weren't aggressive about a resolution of the conflict or Commission Issues.
I Think If Bonanno was able to quel the Families by situating the Leadership problems, the other Families would go along until another NY Family dealt with Bonanno.
Bonanno had a pleasant relationship with the Milwaukee boss prior to Balistrieri. He operated some dairy factories in Wisconsin, so they at least had a working relationship. I do know, Balistrieri made complaints about Bonanno invading territory and was alleged to be involved in some of the bombing in Tuscon.
It's possible Vito Genovese or Tommy Ryan would have started a 2nd Castellammarese War had Bonanno won. West Side would probably not want like another family that's bigger than them.
