Do we require a Multiple entry visa or can we use multiple 144 hour visa free transit permits?

My wife and I have a British and an Australian passport and reside in Australia
- We are flying from Australia to Shanghai and will stay 4.8 days
- We depart Shanghai by cruise ship to Seoul, South Korea for one day
- Then to Beijing for 3 days
- Then back to Korea, Jeju Island for one day
- Then to Kobe and Tokyo where we disembark
- We then fly from Tokyo back to Shanghai for one night
- We then fly back to Australia from Shanghai