USA -> Shanghai 4 days -> Taipei -> Shenzhen

This is very doubtful and this is a situation that is not any more just the case that is treated within 144 hour visa free transit because you are a lawful Chinese citizen with valid Chinese passport, although not yet currently in possession of that passport. Recent experiences show that the Chinese authorities usually allow their citizens holding foreign passports to transit China, so I suggest you not to talk about your Chinese passport and your plans after Taiwan, but just to stick to the transit story where you travel from US via mainland China to Taiwan.

After you reach Taiwan on US passport (you have to exit mainland China on US passport), then you can use your Chinese one as you have mentioned. This is probably the best solution. I advise you to have printouts of your flight tickets on US - China - Taiwan route as a proof that you will be really in a transit through mainland China.