Question on 72 Hour Visa requirements and 24 hour requirements

I'm flying from Atlanta to Taiwan on May 21st arrival in Taiwan on May 22nd. I'm then flying from Taiwan to Shanghai on May 24th. I will then fly from Shanghai to Hong Kong on May 27th. Then from Macau to Shanghai on May 31st and then from Shanghai to Atlanta on June 1st.

It looks like I qualify for the 72 free transit for the first trip from Taiwan to Shanghai and then Shanghai to Hong Kong. It also looks like I will qualify for the 24 hour free transit for the return trip. First, does this make sense and do you think this is okay. The ticket to from the US to Taiwan and Shanghai is on the same ticket. The others will be single purchased tickets. Do you know if this is okay?