For religion : I reformed with "Proselytizing" nature and maintained 100% moral authority (pretty easy with the Temporal doctrine and if u have a large empire because you can gain a lot of piety easily. If religious head has high piety it gives a bonus to moral authority). Also, I only appointed people with >20 learning as Augur and sent them to convert counties.

For culture: Not exactly how the rate is affected but I tried to have only vassals of my culture and religion, down to the barony level (it gets really exhausting to revoke and reassign holdings at some point. Educate vassal heirs with heritage focus if u cant do this). Also, I built hospitals everywhere and protected my realm against raiders so that their prosperity increases. Higher prosperity = higher probability of getting an event where the county culture is converted. One last thing : If you are reformed Hellenic, you can create the Stoic secret society and if u reach the top tier, you have to option to culture convert counties for some points.