Yes, Senusret III gained power over the entire region, including the Nubians as well.
“Senusret III was the first Egyptian king to make Egypt into a true empire by colonizing Nubia, which provided incredible economic benefits that he was then able to use for his many ambitious building projects.”
https://dailyhistory.org/How_Did_Senusr … an_History
He had also divided up his kingdom to be ruled by regional rulers that were under his authority.
And dividing the entire land into thirty-six parts which the Egyptian call nomes, he set over each a nomarch, who should superintend the collection of the royal revenues and administer all the affairs of his division.” 
Which also matches the Biblical account:
Let Pharaoh do this, and let him appoint officers over the land, and take up the fifth part of the land of Egypt in the seven plenteous years.
If one doesn’t believer the Bible already, then none of that adds up to a row of beans
Like I asked earlier, “If the Biblical account is false, then what is the alternative explanation that would account for all of these facts?”
Also, as I mentioned, I’m not claiming all of the archaeological evidence proves the Bible is correct, but they do all lend credence to the Biblical account since the pieces align with it. To counter my claim, you need to either present counter-evidence or describe a viable alternate explanation of all the facts. Simply claiming they don’t add up to a hill of beans does not refute my arguments.
I accept that Canaanites stayed, even if the rule of the Hyksos ended, and if there was another leaving of Egypt, outside the Bible, there is no decent evidence for it that I can see.
Of course the Egyptians won’t record the Exodus, so there will be no direct evidence for it. But, I think there exists some indirect evidence for it.
So it doesn’t prove that they were Hebrew houses, in particular.
Never claimed they were “Hebrew” houses. But they are referred to as Israelite houses, which is good enough in my book.
And I don’t recall that you answered why the Exodus happened after the land of the Philistines
We can perhaps get to that when I discuss the actual exodus out of Egypt.
or why the finding of Moses in the Bulrushes is so like the story of Sargon of Akkad?
The legend of Sargon was written between 1200-700 BC, which is centuries after the time of Moses.
My mother the high priestess conceived me, bore me in secret,
~~in a reed basket she placed me, sealed my lid with bitumen.
She set me down on the river, whence I could not ascend;
~~the river bore me up, brought me to the irrigator Aqqi.
The irrigator Aqqi lifted me up as he dipped his pail,
~~the irrigator Aqqi brought me up as his adopted son.
Date: 1200-700 BC
“A Neo-Assyrian text from the 7th century BC purporting to be Sargon’s autobiography asserts that the great king was the illegitimate son of a priestess. ”
https://en.wikipedia.org/wiki/Sargon_of … rth_legend
So, the main contention would then be when was the Torah written? Was it written before the legend of Sargon was written or after?
Rather like the Ark of Noah is like that old Mesopotamian tale of Ut- Napishtim.
As we discussed, there are global flood stories all over the world.
I’d suggest that this is evidence for an Exilic date for Exodus and Genesis (including the Ziggurat of Babel) and there are two major clues debunking the Exodus as reliable history, leaving an Exilic origin -story for the Hebrews (1) and the hypothesis with better evidential support.
If the Torah was written during/after the Babylonian exile (598 – 538 BC), why would they have constructed a story that does not match the prevailing view of the Hyksos at that time? Manetho, who recounted the history of the Hyksos, lived around 300 BC, and presented them as marauding invaders. It would’ve made more sense to invent a story that matches that prevailing view than invent something totally different.