144 Hour Visa free Transit Starting from Beijing

Hi, My wife and I fly into Beijing from London (LHR) on the 3rd October 2018. We have 3 nights in Beijing before joining our cruise on the 7th October in Tianjin. ( Ovation of the Seas) The first call is Okinawa Japan, then Taipei Taiwan, Hong Kong, Vietnam before Singapore where we fly back from. We believe we are fine with the 144 hour free transit arrangement, but would just like this confirming. Many thanks Pete Smith