Los Angeles (LAX) -> Shanghai (PVG) -> Beijing (PEK) -> Sydney, Australia

I would be having a 13H 20M Layover in Shanghai, and then I would have a 7H 30M Layover in Beijing. Will I be eligible for the 24 hour transit without visa?
Also, on the way back, I would have a 13H 15M Layover in Beijing, and a 22H Layover in Shanghai. Will I be eligible for a 72 hour free Transit? If so, do I find the 72-hour Special Counter in LAX or SYD?
If not, what do you recommend I do? Would I need to get a visa? I don't have any family in china and there wouldn't be any other reason for me to go back anytime soon.