Looking good, Andronicus
Agreed that ducts are high priority.
WRT war, I suggest another third option: Trade away Republic immediately. Then revolt. Dow when China goes into anarchy whether we are out of it or not. This is not as dangerous as your first choice and saves a few turns over the second.
I think it important to let the GW finish in Beijing before taking the town. That plus the Colossus in Athens plus any another wonder equals our GA. Given this, we might as well ally the Greeks to our cause, planning to take Beijing right near the end of the war. I can't see the map from here. Is there any possibility of stealing the horses without taking the city? Possibly using a combat settler?
BTW, according to CAII our net income in Republic will be slightly better than it is now despite the unit costs.
I suppose our next research choice should be Polytheism, relying on the AI to get Horseback Riding.
Edit: Just to be clear, Polytheism is to get out of the Age, not to get Monarchy. If we get the GW, we do not need the Gardens. The FP should complete unless we get an opportunity to rush it. Literature is an optional tech and we should try to trade for it, not research. If we have to, we can come back to it later; there are plenty of things to build in the meantime.