As the guards are corrupt, they are all about themselves first, the well-being of the leadership (so long as it benefits them) second, and the well being of the city a distant third.
The problem with putting them directly under the leadership of the palace guards is it would allow the players to confirm dirty little secrets that would be have only been rumors otherwise.
I would prefer the PC guard faction not be required to patrol, or guard a gate... we have npcs for that. I think they should be a newly formed task force responsible for uncovering "seditious activities". While there may also be such an organization in the employ of the Church of Iuz, the guards would answer only to the General, and can tell the church of Iuz to stick it where the sun does not shine. In addition, should this unit discover the church of Iuz is holding persons of interest, they should march into the temple and take such person into custody. This will be setting up animosity between the Church and the City which could have interesting implications in the future.
Edit: I want people to fear the church inquisitors of Iuz... I want them to be terrified of this guard unit. They should be along the lines of the Gestapo.