Second Kings 17:24-41 was never meant to be about the origin of the Samaritans.

The word Samaritans is used in the KJV of verse 29, but the Hebrew word used there has no T in it, it’s just Samarians.  And it clearly refers to the people who lived here before these Mesopotamians, not them or their future descendants.

I also think it’s important to note that like the entirety of 2 Kings 17 this is really principally just about the City of Samaria, it ends the Northern Kingdom because that was its Capital.  I believe in verse 24 we’ve jumped forward to the time of Sargon II and his one account of what he did here confirms it’s about that one single city.

And Samaria the City was ironically enough never a Samaritan city, it was all through Classical Antiquity the capital of Paganism in Eretz Israel right down to Herod The Great building his major Temples to the Deified Augustus and Kore there resulting in the city being renamed Sebastia.

Ezra and Nehemiah refer more to these Pagan Gentiles living in the land, now definitely in Cities plural, seemingly referring to additional settlement there under Esar-Haddon and Asnappar popularly presumed to be Ashurbanipal.  But those books still never mention Shechem, the city that was the actual core of the Samaritan community.

I’ve recently bought an English Translation of the Samaritan Chronicles and they do not connect their history to Sanballat at all.

But what about Matthew 10?  Doesn't verse 5 in the context of verse 6 confirm that Jesus doesn't view the Samaritans as Israelites?  

What if the Samaritans are excluded form the "Lost Sheep of The House of Israel" classification for the opposite reason Gentiles are excluded?  What if Jesus doesn't consider "Lost" per se?  

What if the Sense of Lostness he's referring to is a product of the cultural influences of the Babylonian Captivity and Greek Philosophy that all three Sects of First Century Judaism have been subject to in different ways but not the Samaritans who have neither the Proto Talmudism of the Pharisees the Epicureanism of the Sadducees or the Pythagoreanism of the Essenes/Herodians?

IDK, that's one possible answer, there could be others. 

While I believe the Samaritans claim to descend form Manasseh and Ephraim, I can't believe the claim their Priesthood authentically descends from Aaron.  Leaving aside 2 Chronicles 11:13-14 and 13:9-10 saying that all the Levites in the North moved South when Jeroboam built his idols, Joshua 21 doesn't placing any of the Cohanim cities in the north to begin, at best Ephraim and Manasseh once cousins of Aaron, the other descendants of Kohath.

Jewish Cohanim are part of Y-Haplogroup J, which is also the dominant Haplogroup among the majority of Samaritan and many other Semitic Populations. My hunch is all of Haplogroup D Patrilineally descends form Abraham or at least Eber. But the Samaritan Cohanim are Haplogroup E. I think Haplogroup E's presence among Jewish populations is via the Mixed Multitude and other naturalized Egyptians and Canaanites.  So those who the author of 1 Kings 12:31 would have unfortunately called "the lowest of the people" would have been those likely to carry Haplogroup E.

There are clearly conflicting traditions meshed together in the currently officially history of the Samaritan High Priesthood.  The High Priest listed as number 9 on Wikipedia is called both Johnathon Ben Abiathar and Ben Hezekiah.  It's clearly they originally just claim to be the rightful descent from Abithar and to just be rejecting Solomon's Temple and the Zadokites.  But later they decided they wanted to reject the Tabernacle at Shiloh as well and so moved the break off point further to disown Eli.