For a more religious reformed/ex Hegemony, I’ve been thinking of a few ideas.
Based on the administration of Sassanian Persia or maybe the early Caliphates (or maybe Paul Maud’dib, fictionally speaking), the bureaucracy and priests should be combined into a single order, or at last be so interconnected that it is hard to tell them apart. This, first, creates a pillar of government that should be solidly loyal to a religious icon MC. Second, education and training for government posts can be combined with religious education, which can be spread and set more easily than a bog-standard university.
The second thing would be a new institution. By coopting the priests, the MC can solve a lot of problems in taking over the Hegemony, but the nobles and holdout Karagond priests will be a problem (along with certain merchants, presumably). So, instead of relying on kryptasts to ferret them out, a more public “secret” police would be formed: an Inquisition, for lack of a better term. Their job would be to hunt down and very publically arrest suspected traitors and heretics against the new Xthonic doctrine (though any treason against the Eclect would be heresy). This would hopefully cow the remaining nobility and recalcitrant priests into submission, but it would also serve another purpose: keeping the newly liberated helots and yeomen afraid of these potential conspiracies. Their new freedom flows down from the Eclect and his faithful, and no one can be allowed to ever forget it.
A religious “counterweight” would be applied to pretty much all high offices: provincial governors will have to deal with specifically chosen archimandrites and High Inquisitors that are roughly equal to them in status, generals will have “chaplains” that they will have their decisions approved by, and they will just control the bureaucracy and local services outright. Everything good and useful will come down from the Eclect (marriages, naming newborns, even tax returns will be done in his glorious name), while “secular”, provincial authorities will handle the more unpleasant stuff (taxes, police work, etc). The goal is to create a situation where the Eclect and his direct agents are always revered, even when the government itself is not.