Egypt had been invaded by Europeans and Southwest Asians several times before the Arabs came over and the Coptic identity formed, so those Egyptians who became Copts would still have been mixed by the time of the Islamic conquest.
Yes, but the problem is that for most of Egyptian history they were moving into the most densly populated country possibly in the world at the time. If one is to assume fundamental changes in the demographic composition it really is the hardest case, simply because there were such a lot of Egyptians. I.e. there just wouldn't be enough people to radically change the Egyptian ethnic makeup except very slowly and very gradually, unless we throw in some kind of ad hoc-hypothesis about the Egyptians either stopping breeding, or being massacred in record numbers, neither of which there is any indication of.
That's not to say imigration hasn't impacted it. Your problem, which is perennial in discussion about race-as-nationality, would seem to be that you want to fix a point in time as zero hour where demarcations were clean, when the ancient Egyptians were specifically "black". (Though since you actually refer to them as East African you have radically extended the application of "black". To me it resembles certain "race-maps" of the world from the 1930's extending the "white race" all the way down East Africa, to Swaziland. I.e. this is a bad idea, and it can be played both ways, since there's a continuum, and East Africans have from time to time been regarded as "white" by those inclined to try to define human races.)
You yourself has pointed to what's considered the likeliest scenario for the original large scale settlement of the Nile valley, the drying up of the Sahara. The general assumption is that people would converge on the valley from all direction but north. So already there Egypt has a probable character of a melting pot. You seem to want to make it exclusively about the southerners, who may or may not have been numerically dominant. The thing about Egyptian geography however is that it's the delta that can really support a huge population. So even if Egypt was unified from the south, which I agree on, you now seem to have to radically downplay what was after all the bread-basket of the country and an as far as we know the great prize for the southerners, and an equal partner in defining Egyptian kingship, the Land of the Sage, Lower Egypt.
The Nile vally in general was a Great Attractor of people through its history. In all likelyhood is was the same in prehistory. Once in the valley, the ability to support a large population would allow groups moving in to increase their numbers, but not faster than those already established. This does allow for slow gradual shifts in the composition of the population, but since ancient Egyptian civilisation was an ongoing process, it also becomes unclear why some, "black" or East Africans", should count but not others? Obviously there would be people one might consider either/or "black" and African contributing, in particular the kings of the unificstion, but why possible other groups should be excluded begs the question?
As far as I can tell, the most probable assumption is still that Egyptians today look pretty much like they always have. I.e. people tend to have darker complexion the further south along the valley you get, looking east African if you like, and on occasion "black" in a western conventional sense. Just like up at the Mediterranean coast they look, well, mostly like people around the Med. And the things is that according to what we know of how the ancient Egyptians figuered their own identity, things like this didn't seem to matter.
