Some minor FYIs/points
-In 3059, the Duke of the New Syrtis and Minister of the Capellan March was still Morgan Hasek-Davion. George Hasek didn't take office until 3060 after word reached of his father's assassination reached the Federated Suns. While he probably temporarily took command of the March (or shared the powers with his mother) during his father's absence it is unlikely that he would have invaded the Capellan Confederation without his father's okay. That doesn't mean he couldn't have tried to reclaim independent Chaos March worlds.
-Shattered Sphere doesn't provide any mercenary deployment for the Federated Suns or the Lyran Alliance. The reasoning given is: "No mercenary units were included, as they will fight for the hand that feeds them." (SS, p26) Of course that claim would later prove to be false.
-The Ministers of the three Marches (well four now) are not automatically given complete control over all forces within their respective Marches. The High Command or a local noble may retain direct control over certain units with the High Command retaining control over key units and local nobles retaining control over their personal units (ex. Duke Stephenson retaining control over the New Ivaarsen Chasseurs). Of course, the Ministers are powerful individuals who can influence units to support them as Duchess Hasek did in the years leading up to the Victoria War (it didn't help that many AFFS military leaders were not happen with leaders on New Avalon especially their lackluster efforts to rebuild the AFFS after the Jihad).
-The Capellan March did not have sufficient military strength to both retake the Sarna March and defend their own territory from a possible Capellan counter-attack (and a possible Taurian invasion as well).