Trying to do two trips in Chengdu

I am planning to do two trips, within 6 or 7 days, in Chengdu using the 72-hour transit free visa process. My question pertains to certain airports. I have a lot of free time at the moment so I will be departing from Taiwan, going to Chengdu, then flying to another airport.

Is it possible to fly from Taiwan to Chengdu, stay for the 72 hours, then fly to Hong Kong? And then after Hong Kong, fly to Taiwan, back to Chengdu for 72 hours and then fly to the US?

Or do I need to fly from Taiwan, to Chengdu, to Bangkok (as an idea)...then from Bangkok, to Hong Kong (or Taiwan), to Chengdu, then finally to the US?

Thanks!