Beijing 72 hour free entry Does a plane change count as a stopover?

I have a ticket Tallinn - Beijing (Aeroflot so a plane change in Moscow).
Then less than 72 hours after arrival in Beijing I fly:
Beijing to Melbourne (with a plane change in Changta CHINA - Hainan Airlines).

Do I qualify for visa free stopover in Beijing.

i.e. Does that change of plane in Changsta mean I am not deemed to depart from the same city. For clarity, my luggage is checked in from Tallinn to Beijing and then Beijing to Melbourne.

Help please. The Chinese embassies in London and Tallinn have not been helpful. Aeroflot say 'speak to China'. Visa cost is €200 for the family so I don't want to pay if it is not necessary.