Looking at flying GEG-SEA-MIA on Tues 10/30. AS697 (GEG 7:50p - SEA 8:57p) is currently $65. AA1471 (SEA 10:28p - MIA 7:15a) is $157. Google Flights is able to combine these into a single reservation, bookable through AA, but the price is $823?! Is there any way to book this itinerary at the lower price? If I purchase separate tickets, I wouldn't be protected in case of a mis-connect, or be able to check luggage all the way through, correct?