travel at the end of Chinese Visa

I have been working in China for 8 months and will have my business F expires soon. My company is purchasing my flight back to the USA through Shanghai. I would like to visit Korea before traveling home, but my return to Shanghai would be after my current F is expired. Do I qualify for 72 hour free transit if I fly Seoul to Shanghai, and then Shanghai to the USA? (staying less than 72 hrs in Shanghai. Also, I think my flight home might connect through Beijing - so it would be Shanghai with Beijing connection (a few hrs) then to USA. What are my options? Thank you!