American Airlines has round-trip flights from Dallas (DFW) to Seoul (ICN) for $873-$888, NONSTOP. Flights October to April. Extended weekends available.
A Carry-on bag and also a personal item is allowed for free on American. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.
Read More Nonstop Flights: Dallas to Seoul $873-$888 r/t [October-April] – American Airlines