Good thoughts but not. The Christian Church is not the replacement of the Jewish Covent with God; it is a Covent to allow non-Jewish the same dignity before God. Jesus was pointing out the political corruption of Israel who was under Roman occupation. A nation occupied and beholden to those who rule them is not sovereign in her own right.
Thus we are left with the Jewish people under the Law, and the Christian religion(s) run by the Pope, and the various non-Catholic denominations.
No religion can be sovereign. Each man, woman and child is. It is that individual alliance to Jesus, or to God as be it that dictates where we go. For the Jews, they don’t have that concept of Heaven but do see Hell.
The New Covenant is not just for non-Jews. It is for everyone -- Jew and Gentile, slave and free, man and woman.
As for the Old Covenant, no one was saved by it. No one could be. Its yoke (the Law) was too heavy.