Will This Itinary Qualify For Two 240 Hours Visa Free Transits

I am an US citizen planning an Asia trip originating from the US. My trip will endup in Hanoi before entering China. It will entail separate ticket segments as follow:

HAN - SZX - TPE ( 1st 240 hours visa free transit )
TPE- DYG, PVG - HND/US (2nd 240 hours visa free transit )

I will be spending 3 - 7 days at each city. I either fly from PVG to HND to catch my flight back to the US or fly directly from PVG back to US.

Please advise if this is an allowable itinerary for 2-240 hours visa free transit. Thanks so much for your assistance.

Angela