US-Shanghai-Singapore-Shanghai-US

Hi. I have a sort of complicated travel question that I am hoping someone can help me out with. I am traveling to Shanghai from New York. I have two round-trip tickets: Shanghai to New York (and back) and Shanghai to Singapore (and back).

I am flying from NYC to Shanghai on 2/18. I will be in Shanghai for 3 days, then fly from Shanghai to Singapore. I will spend 3 days in Singapore, then fly back to the US, transiting through Shanghai. The tickets are on two separate itineraries. Can I use the free transit for this? I am able to present an onwards ticket to Singapore when I arrive in Shanghai. On the return trip, I will fly from Singapore to Shanghai, have a 5 hour layover there, and then fly back to New York. I will not leave the airport.

Any feedback is welcome! Thanks.