Just curious, why not route from KIX to PUS, and then to CJU? Or even go to Fukuoka and then straight to CJU?

To answer your question, immigration is usually a breeze. I haven't had to wait more than 10 minutes and this was during a time when large number of people were arriving. A tip someone wrote earlier is to stay in the Foreigner line that is closest to the Korean Citizen line. Korea Customs will move people over from the Foreigner line over to the Korean Citizen line to get everyone through quickly. So be prepared for that opportunity.

Earlier I wrote that taking the airport express was a good option. Well the limo bus is also a very good choice as well. The advantage is that it will take you direct to the departure level entrance. Compare that to the airport train where you have to walk someways from the platform to the check in desk. Anyhow, you have multiple options.