I feel for the OP. Personally, I do think the advertising is deceptive. Especially if there is no date for a year where there is availability. That is simply un-acceptable.

If I were the OP, I would kick up a fuss on the phone line (when you manage to get an agent again), and do not hang up until you get a confirmed booking using your miles. CX is good that way, the computer used by the frontline says no, but the supervisors or whoever else have a lot of flexibility they can exercise.