When I've cancelled in the past and had others interested, we did it two ways. One person had the capability of conference calling and we were able to work things out that way. Downfall to this is that the person hears your personal information which you've got to give in order to cancel.
The second was a neighbor who was going at the same time and we experienced a bit more of a fiasco. In order to cancel, you get transferred to someone in group dining who has the authorization to cancel and put through a credit to your charge card. With my first attempt, i couldn't get through to group dining...was on hold a long time. Second attempt, I got right through. My neighbor, in the meantime, was on with a rep from WDW DINE who was looking for the cancelled reservation to pop up and snag it.
There is the possibility that someone else can be querying the system at the same time and get the cancellation, but the above methods are what worked for me.
Good luck!