That was...never really in the cards. Most of those territories were ill-garrisoned anyway, and as the Herakleioi in Africa and Gennadios a generation later show, functioned as basically semi-autonomous entities due to the distance from the capital if nothing else. What, exactly, did you have in mind, that would change the nature of these territories from Exarchates to [insert x]s? I'm not sure how this would save money at all. Plus, wintering north of the Danube in 602 was a security mechanism as much as a cost-saver, intended to weaken external raiders. Wouldn't it simply be better to either erase the famine a few months earlier through weather manipulation, or to have Petros successfully crack down on Phokas' mutiny?
Also, there's no way in hell the Sasanians would get killed by the Arabs without the 602-28 war (I also might object to your teleological lolislam, but it's semi-reasonable to postulate that by 602), and definitely no way the Byzantines could conquer that territory, even if they wanted to. And why would they want to take over Arabia...?
Anyway, I disapprove on realism grounds.