I need to extend my visa before Thursday. I just heard that it takes 5 working days to extend a visa, but I need to take a flight to Fujian on Thursday.

Is there any way to quickly renew/extend a visa in Kunming?

Try Dali. I have had my visa there renewed next working day and some have reported that you can get it same day.
I have never had any luck getting a visa renewed any faster than five working days here in Kunming — and since it is now weekend and May Day holiday coming up, you would be lucky to see your passport again before May 4th.