So after another hour on hold I was told my reservation had to be changed through some special highly complex process that would require transferring me to multiple additional departments because it was such a very special sort of reservation. Gee whiz, it was just a codeshare booked on their main website! Several holds and transfers later they just disconnected me. Although they had taken down a number "in case we are disconnected," they of course did not call back. So I went online to just cancel the whole thing. This seemed to work.