Alaska has round-trip flights from Dallas (DAL) to Seattle (SEA) for $177, NONSTOP. Flights April to May. Departures on Tuesday, Wednesday, and Saturday. Origin/Destination reversible.
Note: Carry-on bag is allowed for free on Alaska. You can avoid paying for seat selection by accepting the randomly assigned seat at the gate.
Note: Spirit has flights for about -$21 cheaper, but those aren’t going to be worth it if you need to bring a bag.