I totally understand that there is no way to completely identify the Lost Tribes today, but should there not be a process in place by Israel to accomodate and/or accept their "lost brothers" back to the Land when the Bible prophesizes it will happen...or are you relying on Messiah for this? After all, Israel is just that...Israel (all 12 Tribes/Brothers, not 2 or 3). If not, should you re-name the Land Judah instead of Israel until all are represented?
There is a dispute in the tenth chapter of the Mishna tractate Sanhedrin, between Rabbi Akiva and Rabbi Eliezer whether the ten lost tribes will ever return or not and the Talmud does not reach a clear conclusion about what will really happen. The Ran ibid says that the dispute does not apply to the days of Mashiach and they will return. The Ridbaz (8; 85) also believes that they will return though he acknowledges there are other opinions. In any event some of them were already returned by the prophet Yirmiyahu (Megila 14b) Since we have no clue where they are and what really happened to them we treat all those which are not known to be Jewish as non Jews (Yevamot 17a) On a practical note there is not much we can do and we are awaiting Mashiach to tell us how to go with this issue. There is a rabbi – Rabbi Eliyahu Avichail from Yerushalaim who spent his life time researching this topic and to try to locate the lost tribes – and to a degree with some success. He established an institution called Amishav and you should try contacting him to gather some more information about your question.