There were two exiles. The people of both the north and south kingdoms both spoke Hebrew (and other languages). They were all cousins, descended from the same patriarchs, and of course they intermingled. But the northern kingdom was exiled hundreds of years prior to the Jew’s captivity by Babylon. Where one was living at the time of the conquests would certainly have determined his fate, but where one lived was primarily determined by tribal geography. You focus on outliers.
The Lord has always taken those who sincerely seek him, and that would, of course, include those of the errant northern tribes who chose to center their lives around Jerusalem.
If you’re trying for broad definition of Jew, you must include those of Moab and Canaan whose bloodlines flowed through the Messiah, a precursor for those of us Gentiles who would also be adopted into the family.
Seems we’re talking about two things here: Genetic Jewishness and metaphorical. I’ve enjoyed the discussion. Must go now.
**Moab and Canaan**
The bloodline is traced through the fathers, not the mothers. So Rahab and Ruth aren’t viewed as bloodline.
Also, God told Moses that he is the God of Abraham, Isaac, and Jacob. He didn’t mention Ishmael or Esau in that declaration. The male bloodline of the Messiah was unbroken descendants from Abraham, Isaac, and Jacob.