POD: 647 North African Rebellion

So, I've been thinking of an idea for a possible TL lately. One where in 647, ~something~ (relatively minor) allows Gregory the Patrician (exarch of Africa who declared himself emperor of Byzantium) to be successful at the Battle of Sufetula against the Rashidun Caliphate. OTL, Gregory was killed in battle, so averting that doesn't require any drastic changes.

My problem is this: I've been able to find little on the Internet regarding the details of the battle itself (excepting that the Muslims had 40,000 troops according to Wikipedia), and I know little about the political organization of the Rashidun Caliphate.

So, I have three main questions:
1) How likely would it have been for an army based off of (roughly) Tripolitania to Eastern Morocco to have repulsed the Muslims long enough for an uneasy peace to settle in?
2) How likely would that same army (possibly with aid from the Visigothic Kingdom) be to campaign successfully against the Byzantines (not Anatolia, more likely in Exarchate of Ravenna)
3) How far weakened would Byzantium have to have been to have suffered a large scale defeat at the hands of the Arabs?

I'm pretty sure that you all can see where this TL would generally be heading.

While I might be able to find some way to more or less handwave number one, the other two are much more important overall. Any help is appreciated!
 
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