Will we qualify for a transit visa?

Hi there,
We are visiting Vietnam in October and flights including Beijing were cheaper. Our flights depart Auckland, New Zealand to Hong Kong, then Hong Kong to Vietnam return, then Hong Kong to Beijing, Beijing to Auckland. Would this itinerary qualify for the transit visa?
Also if flights are on time we actually arrive Beijing on a Wednesday 12:20pm and depart on the Saturday at 1:30pm so technically 73hours in Beijing, but surely less than 72 outside of the airport. Would that qualify or should we try to change for a later/earlier flight?
Thank you in advance.
Kirsten