Answered by ZUPAN | Nov. 28, 2019 14:00
In reality, the only portion of your entire itinerary that really interest Chinese authorities is:
Salt Lake City - Shanghai - Singapore
In reality, it will not be Salt Lake City because there are no direct flights from there to Shanghai, but I assume some other US airport from where you will really depart to Shanghai. I hope I'm right because you are not allowed to have any additional landing within mainland China.
This itinerary is definitely eligible for 144 hours visa free transit in Shanghai area and you don't need any kind of visa.
Your return flight from Singapore to Salt Lake City via Hong Kong and again some other US airport is not of interest for Chinese immigration because Hong Kong has its own, distinct immigration authority and US citizens can travel to and stay in Hong Kong visa free.
To conclude, you are really fine for this trip.
By the way, 72 hour visa free transit in Shanghai has been replaced by 144 hour visa free transit a couple of years ago. Also, this is not "72 visa", but 144 hour visa free transit or in other words you will travel through your entire itinerary without a visa.