Kunming stopover before Shanghai

Hello,

I am flying to Shanghai and will be there for 5 days before flying home to NZ, which makes me eligible for the 144-hour transit visa.

I however have an 8 hour stopover in Kunming before arriving in Shanghai which apparently complicates my plans to use the 144 hour free transit in china.

Is there such thing as a 5-10 day china visa that I can obtain? Or can I use the 144 hour free transit in this case?
Thanks!
Jay