I think this was Vito Genovese all the way. He knew that Anastasia wanted revenge for Costello and he was also the boss of the only family in NYC that was powerful enough to challenge his. Genovese probably wanted his own guy to take Anastasia's place, so he got Gambino to hit Anastasia with the promise that he would back him as boss. As for who did the hit, it makes more sense that Gambino would use his own people (I believe that it was Stevie Coogan Gramatura, one of the Armones and an associate Whitenburg) to do the hit. Anastasia was not the most popular boss within his own family so I doubt that it was difficult to find people in the family who were willing to do the job, and by farming the work out the Gallos he would be involving another family, making it more likely that word might get out on the street and make its way back to Anastasia. After Anastasia was hit Armand Rava, Dellacroce and John Riboloto were members of the Gambino family who opposed Gambino becoming boss, but after Rava and Riboloto were hit, Dellacroce was left on his own. Somehow he made peace with Gambino and he became a captain, not the underboss, as Joe Biondo was Gambino's first underboss.

Anastasia's brother Tony did not want to work with the regime either. Interestingly, Anastasia was talking with the FBI at that time, the transcripts were on the Smoking Gun website, and maybe on the Marry Ferrell site. According to Anastasia, Gambino hung him out to dry and let the Genovese, through guys like Tommy Eboli and Joe Lanza, try to muscle in on Anastasia's turf on the Brooklyn docks without giving him any backing. Apparently, Anastasia eventually went crawling back to Gambino and gave him what he wanted because the Genovese never got control of the Brooklyn docks.

As for the Trafficante/Lansky scenario, those two did not always see eye to eye as Trafficante resented Lansky because he was the only mob guy who was bigger than him and closer to Battista in Cuba. Trafficante's lawyer said in his book that Trafficante told him that he needed Anastasia to provide financing for a new hotel that he wanted to build in Havana. Apparently he was in NYC the day that Anastasia was hit because he was working out the details with Anastasia on the hotel financing. With regard to Lansky, he may have been a power in his own right with his own muscle in the 20's and 30's, but everything that I have ever seen indicates that by the 50's he was nothing more than a workhorse for the Genovese. I don't think that he would have had the power to order a hit on an NYC boss at that time. The Genovese through guys like Alo and Gerry Catena had a pretty big piece of anything that Lansky had in Cuba and everywhere else, and they were probably the family with the biggest interests in Cuba. So if anything Lansky may have found out about the Anastasia/Trafficante deal and let the Genovese guys know. Lansky and the Genovese would not have wanted that deal to go through because if it had Trafficante may have surpassed Lansky as the biggest guy on the island and the Gambino family would have challenged the Genovese as the biggest family on the island. Anastasia's ambitions in Cuba might have been a contributing reason to him getting hit, but most likely not as big a reason as the immediate problems that he presented to Genovese in NYC.