Any organization that checks things shojld be a separate entity and not apart of the religion in question. Preferably atheists so they don't have any bias. Secondly I think creating the inquisition lite should be a separate action and a separate decision.I do personally think Realmer Syncretism is probably the best option - it provides a shared communal tie that will help bond our polity together instead of leaving all the cultures as disjoint, while at the same time its syncretic nature means that local beliefs and traditions will be respected instead of brushed aside or ignored. It also means that there's an organization who's job already involves looking into the belief systems of everyone we encounter, instead of leaving any potential nastiness or subversion festering until it hits a critical threshold.
As for a united religion that has the same problem as having one religion. It's impact on politics and keeping them out of the state. They've already been infiltrated once and thats when they couldn't do as much dmg. One religion with a hand in politics would be devastating if we choose a Centralized development. If it's de Centralized then it's that rulers problem and losing ine planet isn't going to be as bad.
This may not brush off smaller religions but we'd have to change their beliefs to make a more coherent system. So jnstead of eraser, we're just replacing/manipulating faith. Who gets to decide what's OK and what's not for a religion? The MC? The problem with that is the Mc is the religious figure of a faith already so instituting changes coukd be seen as all other religions being subservient to the mcs religion. Sort of an imperial cult and emps being on top of local belief situation.