I have learned to cash rush towns that culture-flip to me based on this game, because Canton flipped to me, but then later flipped back and stayed there. I should have immediately started cash-rushing Temple, &c., to make sure it stuck with me.
Actually, better than building culture is to starve it down and/or rush lots of workers. Rush a bit of culture to expand its borders if China controls some its the 21 tiles, but the citizens are what causes flipping back in most cases. It does depend on which civ has more local culture, but (unless it was a freshly built town) this is something you can't change quickly or at all. Reduce the population, and keep an eye on the flip risk.
What's ICS? I was tempted to go after the Aztecs, but there were too many MPPs in place, and so I let the AI Civs beat each other up while I stayed mostly out of it.
ICS is when you plant cities with only a single tile between them. It is a bad idea for anything except empire-wide culture games, but it lets you pack lots of culture buildings in a small space. For a fast culture win, expand speedily, but lay out your normally spaced towns as best you can so that later you can fill in towns on every other tile. Serious players will rearrange towns taken from the AI, but I'm too lazy to do that. Once you are as big as you'll get (either because of the domination limit or because you don't want to go to war at the moment), fill in towns and build cultural buildings. If you are using ToA, you'll get 8 cpt from temple, library, and cathedral, so with 100 or so towns your culture goes up pretty quickly. Without ToA, you have to build the temple, but you also get the university and maybe a research lab. You won't get everything built in every town, but every town adds to your total.
I opened up a 100k save file from a recent game. I had 2200 tiles, 310 towns (so roughly 7 tiles per town), and 1762 cpt at the end. Perfect ICSing would have 4 tiles per town, but water and mountains get in the way, and I don't rearrange the AI cities, plus I settle a bit looser right next to the capital. Still, it is a very close building pattern.
MPPs are risky, but you can also use them to your advantage. If you want to attack someone without triggering their MPPs against you, make MPPs with everyone they have an MPP with. Then declare war, but don't attack. Leave an easily killed unit alone on the border as bait. When they attack it, your MPPs trigger. Do watch out for unintended ZoC attacks, though. Make sure units with ZoC aren't right on their border, or you may accidentally attack them inside their borders when they move past.
If there are lots of other wars going on, it is riskier, but sometimes worth it. If the other AI have easier targets than me, I won't worry about them. I'll concentrate on my target, and then fill in land left empty by other wars while I fight defensively until the MPPs run out. Usually, though, I'll wait for them to expire before attacking, because I don't like warfare so much.