Can I visit Beijing visa free for 144 hours if I am transiting ?

My family and I are visiting Beijing in August . We are flying from the U.K. ( changing planes in Helsinki ) and will spend 4 nights in Beijing before flying to Hanoi. Our flight to Hanoi requires us to change plans in Guangzhou but we would not be passing through immigration or leaving the airport. Will we be able to use the 144 hour free transit option ? I am concerned that as our flight out is not a direct flight to Hanoi then we may not qualify for the provision. Buying entry permits for the family will cost more than £1000 !!! Thanks