They have the promises now. The promises are their birthright.
Just because the Jews have not recognized Jesus of Nazareth as the Messiah does not mean that their inheritance is taken away or that it is transferred.
Jews within the Church have that claim along with the rest of the Church. Nobody outside the Church can make that claim.
No, the Jews have the inheritance and the promises as Jews - whether they are Jews who acknowledge their Messiah or whether they are Jews who do not.
The Church's belief, now as always, is that the Church (composed of both Jewish and Gentile members) is a pilgrim on this earth, and that only when the Messiah returns in glory will the pilgrimage end.
At this very moment, the Jewish people have a right to claim their inheritance. But neither Catholic nor Orthodox Jew believes that this rightful inheritance can be truly secure until the Messiah sits on the throne of David in glory.
You continue to equivocate. I will not ask you to cite a reference since it is still not clear what you are saying. You appear to say that Jews have inherited by blood the Abrahamic promises, blessings of which the bible repeatedly states can only be acquired through faith.
We agree that Jewish people have a right to claim their inheritance but you did not say whether this would require faith in Christ. Neither did you say whether the Church theologically supports an inherited right of modern Jews to take land away from the Palestinians.