Hmm, one option would be, to differentiate between:
- basic/effective fertility
- food production
- food consumption
- basic/effective quality of life
- (risk of) disease
- plagues
- education
Most of those variables are already in, and interact with each other, but some are lumped up with each other in ... interessting way.
For example: the growth rates in game are basically directly dependent on the delta between food production and food consumption ... but that's a very problematic abbrevation.
In reality population growth is directly related to the delta between rate of birth, survival chance and rate of death. Food... just influences all three, but sometimes counterintuitive.
The first variable could be called "fertility", with a value between 0% and 6% per anno:
6% growth means each woman would have almost 9 kids in the 25 years of a typical generation... even at the height of population explosion this wasn't reached anywhere afaik.
Fertility is influenced by several factors, with education, food surplus, health and wealth of a society being the most important. And all three would LOWER fertility (but would lower other variables even more). Civics on the other hand could be used to influence the effect each of the factors has on fertility, but shouldn't directly influence fertility.
Second variable would be survival... and to make it easy, current health could be used. But health should be decoupled from food production.
Fertility - survival = effective growth.
Now... this would allow for a city to easily grow larger than food production allows... which would result in a famine (similar to how diseases work now). But a famine wouldn't just reduce population but rather weaken it first... increasing the effect of the famine... oh and famines usually produce unhappyness, revolt and war as well.
If a famine combines with a high disease risk ... you get plagues, which can easily reduce a population by 70-90%. On the other hand, surviving a plague could grant a building "resistance to plague x" which allows this city to withstand the same plague much better on the next occasion.
Trying to limit population growth could produce significant unhappyness without the proper civics.