Monothelitism was the attempt by Emperor Heraclius to bridge the gap between the Chalcedonian rites followed by the people of Anatolia, the Balkans, Italy and Africa and the Miaphysite/Monophysite (I forget which one is the proper name) rites followed by the peoples of Armenia, the Levant and Egypt. To sum it up, it was vehemently rejected by the Pope and didn't even satisfy all the Miaphysites/Monophysites. Then, after Yarmouk, when Armenia, Egypt and the Levant were lost to the Muslim Arabs, Heraclius' successors saw no need for compromise and it was deemed heretical in 681 at the Third Council of Constantinople.
Basically, if Yarmouk spelled the death knell not just for Byzantine power in the east but Monothelitism as well, would Monothelitism have more credibility in the aftermath of a Byzantine victory at Yarmouk? Turning back a hostile invasion in a few years under Monothelitism compared to taking decades to push out the Persians under Chalcedonianism - that could be a selling point, at least in the East. Italy might break away or lead to an earlier Great Schism.
Thoughts?