72 Hour Free ETA with new flight booked in Place of Connecting Flight

I am flying from Sydney to Beijing and have an 8 hour layover, then fly to Shanghai and have an 8 hour layover there. From there, I will be going to New York. My question is, I will be arriving in Beijing around midnight (Beijing time) and want to take the time to go out and see the great wall of China but will not be able to do it with my current flight itinerary. Priceline wants $900 dollars to change the itinerary but I see a flight leaving the next day from Beijing to New York for $450 so I am considering buying that flight. My question is, will I be able to take advantage of the 72 Hour free transit with this new flight being booked, or will it cause issue through Chinese Customs?