Genetically speaking it would only take a relatively few “wayward” Israelites several thousand years to spread their bloodline throughout the world… if it is in fact a matter of bloodlines. On the other hand; if it is a matter of heart and obedience then it would not even take that long. After all, we all come from one man, his wife, their three sons and their wives. I am almost certain that several times that many Israelites found reason to leave their Israelite lifestyle and communities and mix with other races, depositing bits of Hebrew blood into all sorts of races, that in turn mixed with others and so on. The persecution of the Jews through out history is a prime example of Jews going into hiding and the bloodlines being “lost”. I know of one person of Polish descent whose family is split in the belief that their true origins are Jewish, and this man is not self-segregating even though he believes he comes from Jewish ancestors. If he is of Jewish descent then his son and daughter are ancestors of Israel; are they not?
As far as the Israelite being a chosen people I agree that “chosen” means different so as to stand out from others. This is the way God’s people would be recognized. If there were nothing different about them, no one would ask ‘why?”. All of the festivals and celebrations and reenactments of particular historical happenings were, at least in part, to make other curious and ask “Why?” (Exodus 12:26, 1 Peter 3:15) There is also the fact that the descendants of Israel where the chosen family through which the Messiah would come. Perhaps that alone is “chosen” enough.