Booking 2 separate tkts: SIN-PEK and PEK-HK-SIN, does this work w/China's 72 hr transit visa?

I am a US citizen/passport holder that will be vacationing in Singapore. I'd like to visit Beijing under the 72 hour transit visa. I found flights that would be two separate tickets, one direct from SIN to PEK, and returning on a separate ticket/different airline that connects in Hong Kong, so it's PEK-HK-SIN. Does that qualify for a 72 hour transit visa? My two concerns are that 1) If HK is viewed as another China city and 2) if it matters that my "final" destination is going back to Singapore where I started.