Less than 6 months on my ARC. What are my options?

I'm an American living in South Korea. When I leave Korea at the end of my next contract, I want to spend some time traveling. I had planned to go to PRC first. However, since I'll be doing this at the end of my contract, I will have less than 6 months remaining on my ARC. What are my options? Should I go to Hong Kong first and apply there? Should I send my passport to the US and apply through an embassy/consulate there? Please help! Thanks.