Far eastern cruise stopping at various ports in China, would a 72-hour Visa-free Transit be enough?

Fly to Hong Kong stay for 2 nights, pick up cruise ship, schedule;
Hong Kong
at Sea
Taipei(Keelung)
at Sea
Nagasaki
Busan
Jeju Island
Seoul(Incheon)
at Sea
Beijing(Tianjin)
Beijing(Tianjin)
Beijing(Tianjin)
at Sea
at Sea
Shanghai(Baoshan)
Shanghai stay 2 nights
Fly back to the UK.

Thank you,

Andrew in the UK.