The problem is, I don't see the counter moving too quickly, so I'm not big on ways to slow it down more. As I usually say, though, I don't play enough these days to be considered a good play-testing source.
One idea I mentioned in the past I still like, mainly because it makes sense to me (i.e., why would a newly created city have a significant effect on the AC when it is razed?):
Thanks for your comments.
In my current game, that counter has me really mystified with its movement.
For example, I razed an Illian (Evil, but not AV) city and the counter INCREASED +3. I just don't get how razing an Evil civ's city would do that, but it did. I was thinking it should decrease the counter because it seems like you are doing something good.
However, I also found that when I razed other Illian cities the counter didn't move or increased 'only' +1. Rounding, I suppose.
I really got fed up when the AI kept rebuilding a barb city close to my borders. I razed it at least 5 times and before I could get an Adept there to Sanctify the city ruins, the AI built another barb city. Finally, I just said the hell with this and dropped a Beastmaster on that spot using the World Builder. Voila, problem solved!
I'll give it another go with Marathon speed and see what happens, but I'm guessing the counter will still seem to move too fast for my game.
I have to revise my previous analysis based on further research:
Now, it appears the counter increases even when Evil civ cities are razed, as Loki suggested. That means the only way you can get the counter to decrease razing cities is if you take down an AV city, which is not an issue in most slower speed games as AV doesn't get founded for a long time.
Again, I just would like to see the effect of the following:
+1 counter Good/Neutral Civ city razed
-1 counter Evil Civ city razed
No counter movement when a barb city is razed.
I really don't think it would hurt gameplay in the normal speeds that much, but would greatly improve those slower speed games.