we recently flew ATL/ICN on Delta--then made connections using Skymiles to BKK. Do you have ID on Delta? It might make sense to go backwards to take US carrier--KAL wasn't bad, but not up to par in business class--only a few more miles than coach. Substandard biz food. service, seating. The ads on TV are nothing like what we encountered--only the initial 'bow" was classy...
I would guess that April is rather popular due to inital spring vacations, flower festival, etc. Ck a tourguide book or website for special events first (think Cherry Blossom time in Japan and so on) I would recommend Queen Hotel for day or night layover nr ICN--"Airport Town" is pretty amusing...they're pretty good for upgrades when avail and have good shuttle service. Local rstaurants are cheap and plentiful!
I can ck the current seat aval on Iddeals.com.uk but no historical info--I'm not sure it's pertinent nor dependable any more.
Good luck!.