None of these people are helping you. But I will. For one I don't give a fuck about Corporate Alaska Airlines. They earn their keep well enough. I'd rather side with the little guy.

This is what you do. You call them, you email them. You write them. You contact them every way you can. You lie and manipulate the story to make it seem like their fault. You tell them they left early. You show them how they placed that note on the hours and changed it without notice. You say they actually left way earlier. Make them out to be liars and someone didnt do their job You tell them you called ahead and you were promised that you would make it. You were promised that your ticket would be fine. You tell them the kiosk was broken. You tell them that while at the airport a staff member was extremely rude and cursed at you and called you names. You create a story and make up the evidence to support your claim. This is called fraud. This is what you need to do to ensure you get your $700 back.

Tell them you already talked to customer service about the issue and they promised to refund you. Get the picture? I am sure you can be clever enough to get this resolved in your favor.