I did my dissertation on late antique Egypt, so I'd be interested in such a timeline.
That said... "Coptic" as a term is somewhat misunderstood. No "Copts" actually called themselves that in late antiquity, as the term "Qubt" is an Arabic contraction of the Greek "AiGYPTos". The educated Egyptian elite, while they certainly spoke Coptic, were very much an integrated part of the broader Roman world, and their interests were closely tied up with those of Constantinople, even with the religious differences that undeniably existed.
For a TL with an independent Christian Egypt, I'm convinced that the link with Constantinople and the Roman world needs to be actively severed by an outside force, be it Arabs or Iranians: and it needs to stay severed for several generations. I think it's very, very unlikely that a spontaneous "organic" nationalist uprising against continued Roman rule would ever occur. In this period, such a thing needs the active support or at minimum the toleration of the major elites, and there's no evidence from the sixth century texts I looked at that this would be at all forthcoming.