US citizen, fly from Japan to Hangzhou, then Hangzhou to South Korea, then back to USA

Yes, you can. Traveling on separate tickets and on unrelated airlines is perfectly eligible as long as your itinerary is an eligible one. As far as I can see, you have chosen definitely eligible itinerary and you are allowed to enjoy 144 hour visa free transit in the area of Shanghai and the provinces of Jiangsu and Zhejiang in the way you like. I would like to emphasize that you should take care that your flights Japan - Hangzhou and Hangzhou - South Korea are of nonstop type, i.e. that they do not have any additional landings in mainland China or some third country of any type.

Thank you so much! Yes, the flight from Japan to Hangzhou, and from Hangzhou to S. Korea will both be non-stop direct flight.