2 layovers qualify for 72 hour Visa free?

Hi,
I am a US Citizen in Japan for 3 months.. I was supposed to have a trip to go on a trip to Vietnam with a layover in Shanghai but it has been cancelled however I still want to see Shanghai.
Is it possible for me to go to Shanghai via 2 layovers in 2 different countries? For example
ON A FRIDAY - NRT~layover in MNL , MNL - PVG
DEPART SHANGHAI ON SUNDAY PVG~LAYOVER in DMK, DMK-NRT
will this qualify for a 72 hour Visa? The flights I have in mind will have me less than 72 hours on Shanghai.
Please let me know. Thank you