My impression also was that DHH was writing a musical version of a Chinese romantic comedy. I don't think Sex and the City was ever mentioned.
DHH writing a musical is a better fit for the story, but this change may explain why some of the thrust seems a bit muddled. When the musical starts, it seems like we are watching DHH's commission come to life. But then the Act II opener says that this musical was written by Chinese people, none of whom are named David Henry Hwang. So is it DHH's vision of what somebody who wasn't DHH would have written? It's a bit too meta and a bit muddled, especially since we've seen half the musical already before Act II begins and upends what we think we are watching.