The atonement is only for the elect. The verses in John 3 do not say Jesus died for the entire world, but only for those who would believe. Your attempt to create a corporate atonement is incorrect, both for Israel as well as for humanity.
Read very carefully what Jesus says in John 3:16, "for God so loved the human race, that HE GAVE". This phrase "He gave", speaks of the death of Jesus Christ, and answers Romans 3:23-26, "for all have sinned, and fall short of the glory of God; being justified freely by his grace through the redemption that is in Christ Jesus: whom God
set forth to be a propitiation, through faith, in his blood, to show his righteousness because of the passing over of the sins done aforetime, in the forbearance of God; for the showing, I say , of his righteousness at this present season: that he might himself be just, and the justifier of him that hath faith in Jesus." God's love is "universal" and intended for the "whole human race", and to this "whole human race", "HE GAVE" Jesus Christ as the propitiation, for "ALL (whole human race) have sinned and fall short of the glory of God", and as Romans 3 says, that only those "that have faith in Jesus" as their Redeemer, can indeed be saved. You are quote wrong in saying, "The verses in John 3 do not say Jesus died for the entire world, but only for those who would believe". It does say that Jesus died for the whole world, but only those who believe can and will be saved. A doctor might have the cure for your life-threatening illness, but unless you go to him for this treatment, you would die. If you did not go to get treated, and you were to die, does this mean that the doctors treatment "failed"? This is exactly like the Atonement of Jesus Christ, if the sinner does not accept what Jesus has done, and they end up in hell, there is no way that Jesus' death did not accomplish what it was meant to, and somehow failed as some wrongly assume.