Hi, Am I eligible for 144 hour free transit in China?

I want to be absolutely certain I can travel this itinerary without a Chinese visa before I fly to Asia:
Fly into Hong Kong, stay 2 nights.
Board cruise ship, sail to Taiwan, Busan, Seoul, Tianjin/Beijing for 3 days/2 nights (about 60 hours), South Korea
Disembark in Shanghai, spend 2 nights (about 60 hours). Fly back to U.S.