Since GnK, on Prince and King settings I can still usually get to a point of having 30 to 40 turns of GA by combining the Chichen Itza wonder with the Leaning Tower and Taj Mahal. Chichen gives you the bonus GA duration, Leaning Tower helps pop out Great Artists a little quicker, and the Taj still gives a natural GA. And somewhere in there I'll usually have also built the gardens building along river cities and done all the other basic stuff.
The problem, now, is more on the higher difficulties. Without those wonders I mentioned, you're obviously a little hard up to have long GA's these days, and on higher difficulties it's far less likely you'll be able to collect all those wonders. In vanilla, this problem on higher levels was off-set by the fact you could collect
any GP's to start a GA, meaning even combat could help continue the GA (Great General spawns); now, without the right wonders, it's pretty tough to get a long GA.
The one area of improvement in GnK for this strategy is that, if you can spam a ton of Great Artists, the amount of turns they provide when burned for a GA doesn't decrease nearly as fast. That said, good luck spawning enough Great Artists for this to be more than a tiny bonus (although a certain Louvre looks a lot better for late-game Persia now
)