ATA has caved and conceded, in addition to refunding the cost of our (cancelled) flight, two round trip tickets to anywhere they fly. I figure the way for us to get the most bang for our buck is to go to Hawaii. I mean, we have to at least approach a $500 round-trip ticket in order to approximate compensation, so I figure we best use them for the farthest/most expensive possible destination. (ATA doesn't fly to Europe or Asia, apparently. Cheap bastards.) So I guess it all worked out in the end. All we had to do is threaten them with a letter from our legal representation.
Now if only we had some vacation time to use our free tickets.