I will often use the transit hotel that is inside Terminal 2 and usually very reasonable ($60 for 6hrs) way to get a private room bed, WiFi, TV, and shower. It’s nice to sleep a bit and shower in peace.

Also, ICN is very efficient and you could easily go through immigration and customs and take the AREX express train to central Seoul and walk around a bit for less that $10 each way. You don’t need to claim your luggage and could have at least 4 hours in the city. The train takes less than an hour and you don’t need to be back to the airport any more than 90 minutes or so before departure.

I am, in fact, on the AREX train this very moment during a 13 hr layover between GUM and SEA.