This is actually pretty damn wrong; Copts were 10-15% of the population even during the earlier Arab periods. Both Shanjool Jiwa in his "Towards a Shi'a Mediterranean", a translation of al-Maqrizi's account of Fatimid Egypt, and Ibn al-Athir attests to this.
And they would be reliable sources? I can cite Herodotus to prove that Egyptians have thick skulls while the Persians have brittle skulls. Doesn't make it true. In fact I will; "On the field where this battle was fought I saw a very wonderful thing which the natives pointed out to me. The bones of the slain lie scattered upon the field in two lots, those of the Persians in one place by themselves, as the bodies lay at the first- those of the Egyptians in another place apart from them. If, then, you strike the Persian skulls, even with a pebble, they are so weak, that you break a hole in them; but the Egyptian skulls are so strong, that you may smite them with a stone and you will scarcely break them in. They gave me the following reason for this difference, which seemed to me likely enough:- The Egyptians (they said) from early childhood have the head shaved, and so by the action of the sun the skull becomes thick and hard. The same cause prevents baldness in Egypt, where you see fewer bald men than in any other land. Such, then, is the reason why the skulls of the Egyptians are so strong. The Persians, on the other hand, have feeble skulls, because they keep themselves shaded from the first, wearing turbans upon their heads. What I have here mentioned I saw with my own eyes, and I observed also the like at Papremis, in the case of the Persians who were killed with Achaeamenes, the son of Darius, by Inarus the Libyan."
Even the Egyptian government (with a low ball estimate places Christians at around 6-8%) that amount of resiliance seems a bit exceptional if you are correct.
Your model has the majority converting rather quickly and then maintain pretty much the same proportion of the population for a thousand years or so? That doesn't seem likely. I could be wrong but I can't see what you propose occuring.