B/X Known World
Various charm spells and modify memory would be key. That’s why I think Order domain clerics. Their spell list is great for what you’re after.This just gave me an idea. Why not make the Magic Corps/Enforcers be Warlocks . . . whose pacts are with the head mage? That's an "easy" way to ensure that you have the power. Execute/Imprison Sorcerers, ban Wizardry and Bardcraft, and restrict other magic to be under your control, like you suggested.
Yeah, they would probably straight out ban worship of all deities and require the State to be the only "worshipped entity", unless the State was capable of having Clerics and Paladins devoted to it. "Hospitals" could be indoctrination centers, where you have to go in order to get treatment, but they also check up on you mentally and make you conform with magic if you differ too much.