Great Job on the Mod.
There could also be things built to counter this affect.
The Soviet Union, China, and many other nations over time have worked militarily to keep their 'citizens' within their own borders.
Culture could be gained and lost for a number of rounds, like a trade, to reflect the cultural impact of lost peoples or gained peoples.
Also, if a small city should be reduced to 0 from emmigration, then 2 things could happen. The city gets the cue to Raze, or the computer converts the city to a ruins.
Internal immigration isn't a bad idea, and should get easier with the advent of roads, highways, railroads, etc. But this would require adapting a new city field. Stability. Cities can be independently happy/unhappy from each other within the civ, and their independent ratings would affect overall civ happiness. Prolonged unhappiness would add up, as would prolonged happiness.