I never "win" the culture war -- just one very specific battle. The capital just goes wonder-crazy after building its first settler. Tiny 'pelago with max water is easiest, but others can be done. Build every cultural building. Keeping the AI from launching was the hardest part. Colossus, Library, Oracle, Bach/Sistine, Shakes, and an early temple/library/colosseum (and cathedral/university, although they weren't QUITE as early) were the keys -- the rest was window dressing (intelligence agency, battlefield medicine, wall street, ...)
For 20,000, you can be massively trailing overall and still win. For 100,000, I would imagine it would have to be at least a large and probably a huge map. And that razing some core AI cities would be an integral part of the strategy. Haven't tried to do it yet -- and probably won't, as the time involved would be astronomical.
A sick ICS and whipping might do it, too, but I can't see the fun in that (not that others couldn't -- just that I don't).
Arathorn