72-hour program: If we spend time in Hong Kong before going to Xian & change planes in Beijing?

We will come into Hong Kong on a cruise ship on 21 March 2015 for tourism. At 14:35hrs on 25 March, we will fly to XA, again for tourism. At 12:00 on 28 March, we fly from XA to Beijing where we change planes. We will not leave the airport. At 17:50 on 25 March, we fly from Beijing to the United States. Can we complete that trip with a 72-hour Visa-free Transit form for the XA segment? If not, what visa do we need and how do we get it? If a 72-hour visa-free form is all that is needed, can we get that at the Hong Kong airport on the day of travel or do we need to apply for that in advance?