1) Just Ask
Sometimes it’s worthwhile to simply ask. Politely, of course!
There is a good chance you can get a first class seat for cheap. If there is room in first class (which takes two things to happen: the seats not already being sold out and there not being many premium frequent fliers on your flight who qualify for an upgrade), then airlines will often sell tickets for seats at a discounted rate.
Just make a simple call to the airline’s customer service desk within 24 hours of your flight and see if any are available.