Steven, you prompted me to do some research on this area and while it should take a while to gather information I thought this might be worth adding as a discussion.

Koreans or 2nd generation

First of all, I guess my question is, is the participant Korean or non-Korean?

Because there is a great program facilitated by the "Overseas Koreans Foundation" (OKF)

One is for young adults and one is focused on providing vocational skills to 2nd generation.

Unfortunately their site is only in Korea. 

Non-Korean (foreigners)

If you're looking for programs for non-Korean teenagers who are interested in learning Korean such as language summer camps, so far I found this site that lists a few. But I'll add up as I discover more.

I invite anyone who might have good information to share.

Go abroad.

Two in One

Another alternative would be to join an English ministry program for mission programs in Korea.

http://www.onnurienglish.org/

Email: admin@onnurienglish.org | Phone: +82-2-3215-3686

Onnuri English Ministry (OEM) is one of the largest English ministries in Korea. I believe they might have some information if not their own program.