I imagine a Islam more influenced by the orthodox church. Maybe the Islam in long term absorb the orthodox christian structure with priest, monks and etc (I don't, know more names of christian clerigy in English). Certainly the Greek like the Persian was adopted by the Byzantine islamics, principaly after the Arab-Greek chism. I don,t cred the orthodox Byzantines survives more time in Carthage, possibly they are conquested by Arabian, Berber, Greek islamics or, with a good look and division with Arabians and greeks, the normans.
In more long term I don,t know how time the Byzantine Caliphate resists. The Turks, converted by Arabian Islam, are a one great possibly of the conquest and destruction of the empire. Maybe de varangian/Rus islamics(or Jews or orthodox) or slavs enacting like the Turks in abassid Caliphate. "A Saqaliba Basileos of the Rum."
About Spain, are two possiblys: 1) the islamics not invaded because they are concentrate in conquest the Balkans;
2)the Arab/Berber invaded the Spain because they no are more relation with the greek campaign. I personally prefer the second option: two Muslim empires on the Mediterranean. Maybe together a Greek crisis (bulgarian, Rus, varangian, Turks invaded, Frank crusades, etc.) more Greek emigrate to Al Andalus.
*I don,t speak English very well, but don't exists a good page of alternate history in my language.