U.S. citizen flying from U.S. to tour HKG, PEK, HKG, KUL, HKG & back to SAN. Do I need a visa or can qualify for the 72 hours free transit in Beijing ?

My tour is confirmed on JAL a round trip ticket from San Diego, CA to Hong Kong via Tokyo. Will stay 2 days in Hong Kong, then confirmed on Hong Kong Airlines a round trip ticket from HKG to Beijing for a less than 72 hours tour in Beijing. Stay 2 days in HKG, then confirmed from HKG to Kuala Lumpur on a round trip ticket for 9 days by Malaysian Airlines. Will stay 4 days in Hong Kong and Macau and return to SAN by JAL.