144 hr visa free transit. (DFW(US) > PVG (China)> ICN (Korea)> DFW (US)

Hi
My wife and I, both US passport holders, are arriving in Shanghai PVG from DFW on April 1st with American Air.
After several days of sightseeing, we are traveling to ICN Korea on April 5th with Korean Air.
On April 30th, we return to US with American Air.

In this case, do we need a L or do we qualify 144 hr-free transit?
If yes, can we apply for 144 hr free transit in US prior to departure?

Thanks for your answer in advance.