I have a slightly different take on corruption: I don't care.
I play Monarch and Regent and I simply ignore corruption outside of my core production cities. I like to play large and huge maps and will often have 50 ~ 150+ cities by the endgame.
My Palace and Forbidden Palace rings of cities are high production and low corruption, generally 20 ~ 40 cities with ALL improvements. These two rings generate 2 turn MA, 3 turn Stealth Bombers and even 1 turn MI.
ALL other outlying cities are all STRATEGIC! They are all for specific MILITARY or CULTURAL advantage.
1) Hold CHOKEPOINTS (Land and Sea).
2) Hold RESOURCES.
3) Prevent the enemy from acquiring land. I would rather have a very corrupt city generate one shield for me per turn then generate fifty for the enemy (even in peace!). The only exception to this is when you are implementing the "Vassal State" strategy described elsewhere.
4) Build access to attack, build access to defend. Allow my troops to move ANYWHERE because it is my land. NO ROP!
4) War BUFFER land. Every hex of my land needs to be taken by the enemy to get to my core cities. Every CORRUPT city will still drain enemy resources to take. Maanwhile, my UNTOUCHED core cities continue to build!
5) Allow MY land to be used for WAR AMONG my friends and enemies WITHOUT me! It is extremely useful to allow my "allies" to use my RR system so that they can immediately fight wars against each other. They can immediatly start losing troops and cities to war instead of slowly moving troops around and making peace BEFORE they can lose resources.
I do build CULTURAL and DEFENSIVE improvements in my high coruption cities - actually ALL my cities. The cultural improvements all add to my score (and improve my FLIP ratios) and defensive is self explanatory (YES, build the WALLS for the defensive bonus!)
While I fully believe that you can fight corruption and increase your production by micro-managing, I find that at the levels I play (Monarch and Regent) it is easier to just optimize your core cities and just ignore corruption elsewhere. I set my outlying cities to automatic governors and then I just PLAY! I PLAY this game for FUN.