Good morning MM
I think you are frustrated as the decision (at this time) has been taken from you. A rubbish analogy but the best I can do at this time in the morning - I go out for dinner and see the the specials board, you can guarantee that I will suddenly crave and really want the item that has been crossed off as they have run out.
I think if I was in your shoes I would go along to the Invicta/MGGS open mornings to see them again - it was last year you went wasn't it? If you and your dd think one of these schools is more suited to her than RGS then appeal. You have nothing to lose - yes it will be a long and stressful journey. Your head teacher sounds like he would be a fantastic support for evidence etc and you know in yourself that you are strong enough to do an amazing appeal. I know it still won't have any guarantees but I think it is worth a shot.
Your DD got some amazing scores there so a huge well done to her for working so hard for that
Hugs to you and DD xx