The maximum Byzantine victory over the Persians should be accomplished in the same way that the best Byzantine victories all are -- sneakily.
Thus ...
Emperor Maurice is a bit less hard on his soldiers, so Phocas never overthrows him. This butterflies away the Byzantine-Persian war of 602-628, as Maurice's overthrow was the pretext for the war, Khusrau of Persia having a personal relationship with Maurice. Persians happily fight Hephthalites and Gujaras in the East instead. This allows Maurice and his son-and-heir Theodosius to slowly improve their hold on African and Med. island lands (probably not worth it to keep fighting for Italy).
So then 638 rolls around, and Theodosius' son (call him Davos) is co-Emperor with his father, when the new Rashidun Caliphate comes knocking. Instead of fighting, Davos -- one smart Byzantine cookie -- confuses the issue, mentions that Islam and Christianity are "closer" than Islam and Zoroastrianism, and nudges/convinces/outright-bribes the Caliphate into throwing their full weight against Persia instead of attacking both. Persia is in better shape than OTL because of the "vanished" war, but they still succumb. In an excess of eagerness, the Caliphate then takes over Persia's job of fighting Hephthalites and Gujaras, and plows into India (with many important side-effects not detailed here).
The Caliphate gets so embroiled in fighting to the East, that going to the West becomes thought of as one of those "Oh, eventually, you know" sort of things.
This is the maximal Byzantine victory over Persia. Their ancient enemy is overthrown, without a single Roman life lost. Well, okay, there was a young officer-candidate named Phillipos who died of heat-stroke during the negotiations, but hey.