I recently got my working visa in China. Being a native speaker was a help, so you begin at perhaps some disadvantage, unfortunately.
How is it that you are already here? If you are already teaching in China, then the people you work for should be motivated to help, but there's only so much they can do- especially if the person responsible doesn't know how to proceed with the mountain of paperwork. I had the assistance of a friend with connections in the local government and a native-speaking spouse to fill out and deliver forms. I'd be on my way out of the country if I had to rely on the school for help.
It also depends on the local situation. A city with few foreigners may be motivated to relax requirements (if they can), but no one knows how to handle the paperwork. If there are many foreigners, there may be someone to help you, but there will also be someone to take your place.
Good Luck.