I suggest trying for pku_west's strategy of getting the chinese religions, together with the 2 required religions and Christianity. It envolves researching writing really fast while building SH and then switching to caste system to generate a GS to bulb math. Next you'll want to build Oracle (the 2 required religions should have been founded a little before Confu). get sailing and monotheism from the other civs (Carthaginians start with sailing, mono and alphabet, so you should definetly trade with them). and then get Christianity from Oracle while Researching Calendar like mad with many scientists before the Chinese get it. Using this method I frequently get all 5 religions before 500 B.C, and getting the cities up can be done much easier with more time.
Have you played it on the most resent patch? I have tried this three times and the Chinese always beat me by maybe 10-15 turns. They gun strait for mathematics.