What are my options if my unit is deploying to Korea and my ETS will occur before the unit redeploys?

You simply ETS

Korea isn't like a real deployment. People actually get stationed there. When I got stationed in Korea, I had soldiers ETS from there, the guy whose squad I took over when I got to Korea retired. Korea is more of an overseas duty station than a deployment. While technically the 2 Koreas are still at war, south korea isn't a warzone. When it's time for you to ets, you'll got to CIF and turn in your gear. You'll get travel orders back home and then you can have your household goods shipped to your home as well. You'll outprocess the army like you would at any other duty station, because the army has the infrastructure there to do just that.

South Korea is not a deployment. Your unit is on a scheduled rotation. Like a few others have said, the decision is up to your unit's commander. They can either take you on the rotation and send you home prior to your ETS, or leave you in the rear-detachment to ETS as normal.
Have you completed the required transition program? If not, you will likely be kept in the rear to do so. You are allotted a certain amount of time to outprocess; check with your S-1, or post transition center for details. But first thing you need to do is check with your supervisor(s).

I've been out for some time, but I've never heard of a "9 month deployment to Korea." What unit are you in? I would go...

1. It is up to your Commander. Normally you would be stick in the rear detachment, cause no one wants to pay to have you shipped home early. 2. Instead of talking to us, you NEED to start talking to the Command- it's their decision.

The ARMY's options are: deploy you with your unit and allow you to ETS on schedule; involuntarily extend your enlistment until the end of deployment; reassign you to a non-deploying unit and allow you to ETS on schedule at your current installation.