*sigh* I called the Doubletree back. This time the agent, a nice older lady, was able to bring up the group in the computer, but told me that the Pantheacon block of rooms was sold out. She mentioned a Feb 1 cutoff for booking, but if there were no more rooms left in the block it made no difference.
So I booked the room, for the 4 nights, including the outrageous price for Sunday and Monday. It's $140 over what I'd planned to spend - the price of two memberships. But now I have a confirmation number, and maybe the con people can straighten it out, if the "sold out" thing is untrue.
I then went and joined the Hilton Honors program. Considering that I attend two or more conventions in that hotel a year, I might as well earn points and perks for it.