I suspect Ashley is searching for single tickets - where there are a few slots left. But you want 2 or more tickets where nothing is available until October. Unless the royal quarters are a must-see, I would buy the general ticket, where some are still available for most of September.
The Cuarto Real Alto are not the most interesting part of the Alcazar anyway, so you're not missing too much. If visiting it is "non-negotiable", however, you may need to purchase a tour company ticket. Personally, I wouldn't worry about it and just see the better parts of the Alcazar on a general ticket. But do book that ticket soon since the queues for those buying on the day can be horrendous.