mrs767er, unfortunatly we do not "officially" have a ZED agreement with TG. But, it comes up on myIDtravel and some people have used it with success and others have been denied so I would not like to take the chance.
I would love to take Delta but I would only have 45 minutes to catch the connecting flight and that is probably pushing it and if I missed it it would be 24hrs for the next flight.
I think the ICN to REP is 5 hours or something like that. Problem with going to BKK is UA and DL land close to midnight so would have to wait for awhile to maybe have success on TG. Going thru ICN I would land in REP before the UA/DL flights get to BKK saving 10-12 hours (even more if taking bus from BKK to REP).
Also we are still waiting for KE to inform us if we will get to ZED with them or not. Right now NO
I think the only way for me to ZED to REP is Asiana, or try on Thai Airways and take the chance.

Thanks everyone, from our company website people said that ICN is one of the best airports for travellers and they do have a transit area so you do not have to go outside and back in. Also, they mentioned you can check in at the Asiana gate.