I don't think the problem is the speed at which culture spreads, I think the problem is the game mechanics around culture spreading and how different cultures effect relationships. As things stand the penalty for having a count of a different culture to the county is very small - occasional peasant rebellions that are easily dealt with. As a ruler the penalty for having a vassal of a different culture is quite significant (-20/-10). As such there is a strong incentive for rulers to homogenise their vassals to a common a culture, and a much weaker incentive to homogenise the culture of the provinces.
The way in which culture spreads is driven by the county rulers. The most common spread is if the count is a different culture and an adjacent province is the same culture. I think the whole liege chain needs to be the "change to culture" but I'm not 100% sure about that. So for example Dublin begins as Norwegian, with an Irish ruler, surrounded by Irish provinces. So long as the ruler, and their whole chain up to the independent ruler is Irish, Dublin will change to Irish. If the ruler of Dublin isn't Irish, even if their liege is, then it won't change. I think its possible for the culture to change when the count is a different culture to the liege, but I think the probability is reduced.
So, as a liege there is a strong incentive to make your vassals the same culture as you, which they in turn have for any vassals of their own. I generally put quite a lot of time into homogenising my vassals (by making sure their heirs have guardians of my culture with gregarious/diligent traits) to remove these penalties, which is turn encourages the spread of my culture throughout my realm.
This feels counter-intuitive for the period. So I think this emphasis should be changed around. Counts should want to be the same culture as their provinces, and rulers should have a lesser negative reaction for vassals of different cultures. Something like a levy and tax hit for different culture within the demesne would be a good thing, at the same time perhaps halving the foreigner penalties for vassals. e.g. 20% fewer levies, 20% less tax.