Using 72 hr visa free on a transit that is returning back home

I came to find out Chinese embassy will not give me an entry permit because my passport expires in 5 months, even though I was only planning on traveling to Beijing in a few weeks and staying there 10 days. My plan is to now buy a round trip ticket to Hong Kong, but it would be great if I can make use of the transit policy. Can I first go to Hong Kong, then stop in Beijing for 48-72 hrs, then come back to the US? I have an American passport.