Well, I guess not so much. I took an extreme example by giving myself a huge stack outside an enemy secondary city and capturing it. It was pop 15 when I took it. It was in revolution for 9 turns and shrank to pop 10 before I could build anything. I put it on build culture with my global slider at +50%, and it expanded a couple of levels quickly, but it still couldn't get cultural control of most of its adjacent tiles for a while. After 5 turns of control I culture bombed with a Great Noble. That still didn't help. The city shrank to pop 5 with almost no nearby tiles controlled, before its water income and pop stabilized.
The mechanic I was trying to find is a "Reconstruction Genius", to stop that huge pop slide. Maybe a simple +cul/turn, or even "culture mini-bomb" does not accomplish this. Can anyone suggest some other mechanic to accomplish this?
It depends on the city, and its relation to other culture.
If you take a city that is off by itself, then you need a very small amount of culture to pop to the second level, and work all the tiles in the BFC. This can be easily achieved by using the "build culture" option, which is what I was referring to; you can quickly get to level 2 or level 3 culture, which will let you control any nearby tiles that do not have heavy enemy culture.
If you take a city that is surrounded by other enemy cities, with their culture, then obviously those neighbors will have very high culture levels, and so territory around your newly captured city will be heavily in enemy culture. You can reduce this somewhat by pillaging (influlence-driven war).
Your city will probably starve down a few levels because many of its water sources are now in enemy territory.
This is as it should be! There should not be an easy way to over-turn many years of cultural investment by the enemy. (except a great artist/noble culture bomb). If you take a single enemy city, you should be able to work only a few of its tiles; the rest remain enemy territory.
Otherwise culture is too weak.
If you want to be able to work the tiles, then you need to capture multiple cities.
A mini-culture bomb instantly ends uprising and will get you out to level 2 borders, which is as much as it should be.
A mini culture bomb ability is still very valuable, both in ending revolts and instantly expanding borders. Whereas a +3 culture per turn is very weak.
Industrial: "mini-hurry" ability for +50 hammers once per 20 turns, more or faster with Sapho. Move it where you need a building or unit finished quickly.
I would either halve it to 10 turns or double it to 100 hammers at a minium. Otherwise you are providing an average per turn 2.5 bonus hammers, which is pretty pathetic.
Or some combination of the two.
50 hammers doesn't really build anything here.
Also; the standard great engineer type bonus hammers can only be used on buildings, not units. Which is fine I think.
Financial: +50% trade route yield or clone the Financial trait of +1 gold on worked plots with yield over 2 gold. Not all that interesting yet.
A possible alternative would be to make it a spice economy specialist, that provides very large tile yields to the harvester improvement.
So you have incentives to ship him around to anywhere that you happen to get a lot of spice blows. Maybe +5 commerce to harvester (when on spice resource).
On a similar line, maybe there could be an Ecologist to synergize with arrakis paradise, that speeds up terraforming locally, and gives a small bonus of some kind for terraformed tiles.
Spymaster: increases spy-catching ability in city, perhaps gives invulnerability to spies, perhaps gives invulnerability to spies for all plots in a radius. Has a small percent chance to generate a new spy unit every turn.
Increased global countersecurity, invulnerability to spies in the city he is in, and a large % boost to espionage point yields?