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.

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 Activity and Greek Philosophy that all three Sect 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.