we went LY end OCt--rather Hot/Humid that year but great loads
Used DL ATL/NRT, frequent flyer seats Korean Air NRT/ICN/DPS
returned KE DPS/ICN day room for rest and ICN/ATL
It is a really long trip for nonrev
Don't know your contracts for zeds, etc
Don't know your gateway but I will be happy to pull up my fabulous stash of info (some from my nonrev brain, some from files) and pass along my knowledge to assist

I will recommend luxurylink.com for some incredible 3-5-7 night pkgs, as well as some smaller places outside of the main tourist areas.
It's a very small island and such wonderful people. Drivers are abundant but I have some personal recommendations if you need them TripAdvisor has TMI but good source if your sort thru it. Keep in mind most travelers go frequently, so if you want advice on a one-in-a-lifetime experience vs drinking on the crowded beaches with all those whacky Ozzies (no offense intended--it's the fave cheap vacation from what I can tell) I can help. We plan to return next year (it's that good!) but so far away...

You mostly have to connect somewhere halfway plus--westbound is still best option.
Lemme know if I cna help more.