i also think they would make inroads but not conquer anything big , in the lot because they defeated many byzantine armies even though they nearly did and that was the united effort of the caliphate, I would not say a decentralized effort is harder for one than the roman empire dealt with the tribes well even until the fall and the germanic tribes were more than the Arabian ones that and the Arabs can also go Mesopotamia.
also, why is the east in danger due to Heraclius' religious policies if by that you mean the myth that the copts embraced the Arabs as liberators I can only say there is no evidence for this and modern academia has rejected the idea
Also unlike the west, the east fell mostly due to fedorati taking advantage of the civil war and even playing a role in them this is not the case with the east, Heraclius' legacy was strong enough that Constans II despite being a boy and the empire being gutted the instant Valentinus attempted to take the throne from the young Constans II he was lynched, the only big rebellion of his reign was Gregory rebellion, and he was only killed was a rumor came about, in a world were Heraclius dies as Hero this would mean Constans II position is secure indefinitely unless he does a major screw up.
Also the migrations would likely being in 640s not in 633 like the otl which gives the Romans 20 years to recover rather than 5 they had so an empire recovers for an extra decade with Heraclius , Constans II another competent emperor takes the throne and what happens next is butterflies