What you are saying is just not correct. If you do a search of the word "Gentiles" in the NT, for example, you will find multiple passages where what you say simply cannot be, and not one passage where it must mean what you say. I am certainly well aware of the division of the kingdom and the later dispersion of the northern tribes, but those dispersed Israelites were not the same thing as the "Gentiles."
Your assertion that the Diaspora equals the "Gentiles" is an unusual, if not unique, view. How did you come up with it, or where did you get it from? Do you have any Bible passages or other evidence to back up your claim?
There are three people in scripture who's life mission was set out before they were born. Jesus, John the Baptist amd Jeremiah. Question - do you know what Jeremiah's mission was?