Because Sonya wrote the lesson plans for our history/geography/Bible curriculum I asked her for her thoughts on this. Sonya looked in the lesson plan guides to see what we had for dates and also looked in the spine book, Ancient Egypt and Her Neighbors.
She found that the Book of Centuries date given in Genesis through Deuteronomy & Ancient Egypt and in Joshua through Malachi & Ancient Greece for the Tower of Babel is c. 2242 BC and the date given in Genesis through Deuteronomy & Ancient Egypt for the unification of Upper and Lower Egypt is c. 2242-2189 BC. Those dates put the Tower of Babel before the establishment of Egyptian civilization. Dating ancient events and civilizations always involves some guesswork and can only be given in approximations, so there can be some variance in dates given in different publications.
In chapter 1 of Ancient Egypt and Her Neighbors, the author writes that “For the next 3,000 years, Egypt would remain one, but they never forgot their divided past.” That sentence doesn’t indicate when the 3,000 years began, just that Egypt remained unified for that many years. Could that be where you have some confusion with the dates?