The thing is, one of the characteristics of late antique Roman Empire was the tradition of soldier-Emperors, starting with Aurelian, going all the way to Theodosius. Such a ruler had to be close to where the action was likely to be - hence Diocletian's capital in Nicomedia, and Constantine's in Byzantium. Alexandria is too far from any major center of action, meaning that any successful general would be more likely to proclaim himself Emperor, and actually have a chance of keeping a large domain. So, I can see Alexandria a Roman capital if either there is a greater threat from Arabia or Africa, or if division of the Empire is into more parts than two. Alternatively, division amongst Maurice's sons (which Maurice had plans of, but never got to due to being overthrown) can work - one gets Italy and Sicily as a reborn "Western Empire", one gets Greece, Balkans, and Anatolia, another one gets Egypt and North Africa.
Since this is right before the rise of Islam, Muhammad would not be butterflied away, and given Maurice's good relations with Khusru II of Persia, probably no devastating Roman-Persian war of OTL. This means that Arab invasion, if it comes, will be likely stillborn, and Islam would be contained early. Where that leads to is anyone's guess, simply because at that point, many different factors are still unknowns. Can the Western Empire retake all of Italy from the Lombards? Will there still be a Persian war in a generation after this one? Will the presence of concentrated Roman power in Egypt preclude unification of Arabia, and result in Muhammad being defeated before he can become a pan-Arab ruler? Too many variables to be able to say with certainty, although one can speculate.