At Seoul's Incheon Airport (ICN), there is a "transit" hotel. I just found their web site (it can take a little work) in anticipation of a return stay. It is inside the security area, so it is perfect for a shower and a short rest while on a layover. I actually prefer 6-8 hours to 2-3 hours layovers for situations like this. If my future plans materialize, I will have 3 1/2 hours at ICN westbound, and 11 hours on my eastbound layover. Neither is ideal.
This is how it works. You do NOT exit security, as if to go to baggage claim - that would defeat the whole purpose. In fact, I don't think they can let you back it until a couple hours before your flight! Since you don't exit, you should be in your room within 30 minutes of touchdown. You get a room in 6 hour "blocks". You have all the usual amenities of a small hotel room including alarm clock and/or wake-up. ICN has plenty of good food and shopping, so you need this room only for sleeping lying completely flat, uninterupted, and showered. Each six hour block will set you back about half for what you would pay for a medium priced business hotel. If you have any doubts that you need the rest, you might change your mind after that 11 hour flight!