The China embassy in Seoul asks applicants other than Korean have to hold ARC valid for at least 6 months, therefore, you can't get a China tourist visa from Seoul. I hear that China consulate in Busan has not applied this rule, you can still apply for a China visa from consulate in Busan with the ARC valid for less than 6 months.

Now, your ARC still has 6 months remaining validity, but you can't apply for China visa so early, the single-entry China visa is only valid for 3 months, if you apply for it now, it expires before you use it, please apply for China visa in January.

Please contact the list of travel agencies authorized by the consulate, and mail your application to it. The consulate only asks for your ARC in Korea rather than your Korean tourist visa.