I just finished the Chinese UHV in my second try on monarch. To get the 2 religions you have to beeline them, but you need BW for chop/whip. There is no time for other worker techs. Send a warrior to the boot of Italy so you can trade with Carthage, Roma and Greece for Wheel and Pottery later.
Tech path: BW, AH, Writing, Math, Fishing, Sailing, Calendar
Settle: worker, worker, settler. Chop the 2nd worker and settler. Settle Shanghai 1 tile above the rice. After writing, build a library in Beijing straight away for the 2 scientists. Build 1 more settler out of each city.
Settle the next 2 cities east of Beijing and start whipping the infrastructure (library and granary). Running the 2 scientist in Beijing gives you a Great Scientist which you can pop for Alphabet. Trade as much techs as you can. Focus on religious techs so you can start building those temples (Priesthood). You need Monotheism for OR the make those needed missionairies
Run 2 priests in the shrine city which has the 2 temples first and generate a Great Prophet to build a shrine, generate another one later for the other shrine.
Settle the next 2 cities south and the other 2 cities up north in the forests. You have to build the last 2 quite late, otherwise you don't get to Music in time.
The hardest part is getting the 120 units in 1600 AD without crashing your economy. Merchant specialists and the two shrine cities are the key to making it. Currency (market), Guilds (grocer), Banking (bank) and even CoL (courthouse) are all needed to keep you economy afloat.