I like China, and for the reason given – it's fun to play the long game while dozens of other civilizations come and go around you. I've played several China games in different versions, since finding this mod in... wow, 2012. It's my way of getting oriented with whatever's changed before playing something unfamiliar. The first time, I remember you could poach most of the good classical wonders as China, which hasn't been viable for years now.
I think the first two UHV goals are excellent. They pull in different directions, requiring a good pace of expansion while maintaining a decent economy so you can lead on tech in the medieval era. But I've never cared for the third goal, and still wish it were something different. It just seems to me that it invites the player to phone it in as soon as they've fended off the Mongols – grinding out great people for golden ages is uninteresting. I feel like an ideal third goal would be one that asks more of the player in the 1000CE to ~1600CE period. For this reason, I always do the first two goals and ignore the third, inventing objectives of my own for later in the game.
Four golden ages can be done on monarch/epic before 1000CE, by the way, although it might require unconventional play. I haven't done it myself, but I have built more than nine academies/shrines/administrative centres by that date. First city is Chengdu, second Yunnan-fu, third Qingyang. Also, research mathematics before getting any tech that founds a religion and build the Parthenon for +50% great people birth rate. (This is the only classical wonder I'm sure is still worth the trouble for China. The Great Library is also very good, but the tech that unlocks it founds Buddhism. Even with marble and intensive chopping, the risk is high that Buddhism will spread and waste all hammers spent on it.)
For an alternate approach to the third UHV, I think it would ideally combine an objective that requires internal development with a foreign policy aspect representing China's regional hegemony (so the tributary system). I think the latter aspect is important because otherwise there's a long period where you've already finished consolidating all historical territory without much engagement with the rest of the world, other than fending off one or two northern invasions.