You might also test adding courthouses and police stations to cities far from the capital.
I read that the capital distance was still important for cities located around the forbidden palace and courthouses and police stations each reduce distance corruption by 50% (multiplicative). So after courthouses and police stations are build the corruption in cities close to the forbidden palace should be very low.
If I take a look at the Kua, it seems as though distance corruption is also reduced somewhat by building the FP, because otherwise the corruption in Kua would be higher (Distance corruption from a city very far from the capital is higher than 50%).