72 hr visa on return trip only

On our way to Korea, we will stop over in PEK (but not leave the airport). 4 days later, we will stop over in PEK again. Would we be able to activate the 72 hrs beginning our 2nd stopover (informing them in Korea before we leave), or would the time begin at the first stopover?

Korea is covered under the 6 Asian countries participating, but we have US passports, so I'm not sure if they count the country by departing country or by passport. If they count by passport, technically we arrived 4 days before...