There is an idea to try to change the religion for Rome to Latin culture or the Latin population. For example, you can use the script to link the construction of barracks and some types of cities to the percentage of the population's culture. In my opinion this would reveal the distribution of the Roman population.
For example, a city of the first level can build a Roman culture 25 percent, the second 50 percent. It is also possible to add dependence on the level of religion or the percentage of the population for the construction of union cities. A temple can, for example, be replaced by the level of Roman citizenship or assimilation.