I feel like it's worth explaining how in year admissions work. You can email the council and ask about spaces, but until you've actually done an application (for which you will need local address), the school can't hold a space for you- they have to give it to someone else if they apply before you. The LA has to offer you a school place, but not necessarily at the school of your choice.
You can appeal for a place at a school, and wanting to continue to be educated within a certain faith would likely help your appeal, but if the school is already full/over capacity, then you may not get in on appeal.
You could also go on waiting lists, but people tend to prefer not to move their children after Y10 if they can possibly avoid it.
As others have said, your DD may have to move for sixth form anyway- nearly all sixth forms are selective, and she'll need the right GCSE grades to progress.
I think, instead of focusing on "best", you probably need to find an area where there would be multiple schools you'd be happy with, at least for the next few years. Or if you want a guaranteed school place before you move, unfortunately you'll need to go private.