Alright, let's deal with just one fact and see what happens from there.
You said that the word translated as "Jew" is actually "Judean". While not strictly incorrect, it very much referred to not just Judeans, residents of Judea; nor only to the tribe/kingdom of Judah. A Jew was anyone who followed the Jewish religion, regardless of tribal affiliation. As such the post-exilic works of Ezra-Nehemiah simply speak of the Jews, collectively--the return of the Jews from captivity, and the rebuilding of the Temple. Whether we are talking later Greek or Roman rule over the region, "Jew" was the identity of the people. Jesus, a Galilean Jew, was of the tribe of Judah. Paul, a Jew from Tarsus, was of the tribe of Benjamin. A member of the Diaspora in Rome was no less Jewish than the Palestinian Jews living in Jerusalem.
Jesus is the root and offspring of David = tribe of Judah.
Benjamin is one of the 3 tribes of the the House of Judah.
1 Kings 11:29-32
Ezra and Nehamiah are from the Babylonian captivity = House of Judah.
If both halves of the divided kingdom of Solomon are being mentioned in the same verse... they cannot be the same people.
John 7:1 After these things Jesus walked in
Galilee: for He would not walk in
Jewry, because the Jews sought to kill Him.
Ioudaia = feminine of Ioudaios(with ge(land) implied); the Judaean land (i.e. Judaea), a region of Palestine:--Judaea.
John 4:3 He left
Judaea, and departed again into
Galilee.
Matthew 2:22 But when he heard that Archelaus did reign in
Judaea in the room of his father Herod, he was afraid to go thither: notwithstanding, being warned of God in a dream, he turned aside into the parts of
Galilee.
Matthew 4:25 And there followed Him great multitudes of people from
Galilee, and from Decapolis, and from Jerusalem and from
Judaea, and from beyond Jordan.
... (= more of Judaea than just Jerusalem)
Matthew 19:1 And it came to pass, that when Jesus had finished these sayings, He departed from
Galilee, and came into the coasts of
Judaea beyond Jordan;
Matthew 24:15-21 When ye therefore shall see the abomination of desolation, spoken of by Daniel the prophet, stand in the holy place, (whoso readeth, let him understand)[16] Then let them which be in
Judaea flee into the mountains
This last verse means the time of Jacob's trouble has begun... and ties into the Revelation's Resurrection of the Two Witnesses... where their enemies, seeing them taken up, give glory to God... and head for the hills.
The "lost sheep of Israel" means "the Jewish people"; as Jesus is making the distinction between the Gentile woman and the Jews.
The "lost sheep of Israel" in the most immediate sense simply refers to Jewish people. And yet, the episode of the Gentile woman is an absolutely valuable thing, because if we really are paying attention to Jesus, if we are actually understanding what this whole Messiah thing is supposed to actually and really be about--this Gentile woman is made a member of the household of Israel through this One she speaks to, for He says of her, "O woman, how great your faith!"; not unlike the words spoken to the Roman centurion, where the Lord Messiah says, "I have not witnessed such faith in all of Israel".
That verse in full actually says "the Lost Sheep of House of Israel"
= the 10-Lost-Tribes. ... but Judah wasn't lost.
Nationality: "the status of belonging to a particular nation, whether by birth or naturalization."
BTW, the Bible never uses the term "gentile woman" in that verse... it says she's living in Canaan... that's it.
Matthew 15:21-28 Then Jesus went thence, and departed into the coasts of Tyre and Sidon.[22] And, behold, a woman
of Canaan came out of the same coasts, and cried unto Him, saying, Have mercy on me, O Lord, Thou Son of David; My daughter is grievously vexed with a devil.
And These aren't genetic-Canaanites
Zechariah 11:7-14 And I will tend
the flock of slaughter in the land of Chanaan: and I will take for Myself two rods; the one I called Beauty, and the other I called Line; and I will tend the flock.[8] And I will cut off three shepherds in one month; and My soul shall grieve over them, for their souls cried out against Me.[9] And I said, I will not tend you: that which dies, let it die; and that which falls off, let it fall off; and let the rest eat every one the flesh of his neighbour.[10] And I will take My beautiful staff, and cast it away, that I may break My Covenant which I made with all the people.[11] And it shall be broken in that day; and the Chananites, the sheep that are kept for Me, shall know that it is the word of the Lord.[12] And I will say to them, If it be good in your eyes, give Me My price, or refuse it. And they weighed for My price thirty pieces of silver.[13] And the Lord said to Me, Drop them into the furnace, and I will see if it is good metal, as I was proved for their sakes. And I took the thirty pieces of silver, and cast them into the furnace in the house of the Lord.[14] And I cast away My second rod, even Line, that I might break the possession between Juda and Israel.LXX
