I don't think a fast growth is a path you want to take. I've been experimenting in a lot of ways to stop squalor, and it seems that a city will remain tame when is developed over a certain time.

People often become too hasty in trying to make a newly conquered city a worthwhile addition. But it seems that making too much use of "low taxes", and concentrating too much on tech developments biased(such as military/econmoy bdgs) only seems to inflate the problem.

Never, ever use low taxes. Even if it means a revolt. Cultural differences and Squalor dies out slowly. Also, your buildings need time to build. But the population growth rate is much faster than that when "low taxes" is used. It simply makes the problem worse, since the population rate is rising fast, but none of your key buildings are up yet, and squalor level keeps piling up as the population grows.

The distance to capital factor can't be solved, but the cultural differences can be managed a bit - destroy the religious buildings in the city and set up shrines/temples of your own. Also, destroy other institutional buildings which differs a lot from your own, such as circuses or arenas, if for example a Carthagian army captures a Roman city.

Replacing religious buildings of your own immediately lowers cultural difference about 5~10%. Destroying institutional buildings makes citizen tempers hard to manage in the short term, but in the long run, its much better.

In the end, the most ideal conditions of city growth is when you've built all the buildings needed to be built, and waiting for the population to increase to the next level.