This piece of document will not answer your question regarding the Luciano/Genovese rift. But it´s interesting because it says that Frank Costello was reinstated into the Genovese Family (after being shelved by Genovese) in 1960. Apparently they had a talk and found out that Tony Bender had played them against eachother in order to grab the leading position in the Family.

https://www.maryferrell.org/mffweb/archive/viewer/showDoc.do?mode=searchResult&absPageId=981009