Is it possible for me to apply for a Z visa in South Korea?

I am a New Zealand citizen currently residing in Korea, I have been teaching here over a year and have found a new job in China. I have all the documents required for this job but have ran into a problem. I read online that I needed to apply through a travel agent rather than the embassy itself. When I went to the agent they told me that my ARC card needed to be valid for at least another six months to get a chineses Z type from Korea.
Is this correct? I am unable to get it in Korea because in order to get that I need a job in Korea, but I cant work in Korea because I have a 12 month job contract waiting for me in China. Is it at all possible to get the Z type for china in Korea? I really do not wish to let down the job in China by being unable to work for them at such late notice.

Any help you can provide me would be so greatly appreaciated.