NYC -> Beijing (2 days) -> Taipei -> Beijing (few hours layover) -> NYC?

Dear sir or madam,

I am an US citizen who was born in Hong Kong in the 1980's. I am planning on travelling from NYC to Beijing and staying there for 2 days at a hotel. I then plan to go to Taipei for roughly 3 days. After my stay in Taipei, I will return to NYC, but please note that my return flight connects through Beijing. In this scenario, can I transit without visa? (I guess I will be using the 72-hour exemption for my 2-day stay in Beijing & using a shorter exemption for my layover on my return flight?)

Thank you very much!