Indeed, the website that they suggest/ require that you use does not include Southwest. I did not stop to think of them when they did not show up on the "rebookmyflight.com" (or whatever it is called).

The other issue was that I wanted to get back to the checkin desk as fast as possible to get on the next day's flight before all the seats were gone. They do not have a 'service center' airside. Then after I was re-booked, it was too late to claim the $250 for a different airline.

The trouble with a late day flight is that not only are there fewer options, but also not a lot of time to think things thru.