Have you got any evidence that your dd is achieveing 4a's and a 5c?
I think that is something that would be useful, and what about evidence of good scores from KS1 SAT's?
Are there any academic extra curricular activities you could get evidence from?
Is the school refusing to write a letter because they don't think your dd is academic enough, or is it because they simply don't support the system? If it's because they don't support the system, you could simply say that the school's policy is not to support appeal applications so you were unable to provide evidence from them. If it's because they don't think she would cope in grammar, it might be best not to mention it at all and just concentrate on the other reasons why your dd needs a place there.
I have been through the OFSTED report and school prospectus and highlighted the things that they offer or are strong at that would particularly benefit ds for our grammar school appeal. I have no idea if that will help at all, although I have been advised that we need to let the panel know why our ds will be at a disadvantage if he doesn't get a place, but without being too negative about the other school.
Something you could do to provide academic evidence is get an educational psycologist report done, although it's not cheap and it's not guaranteed to give the results you want. It's only really worth it if it shows a very high academic ability.
Btw, don't rely too heavily on my advice, I'm just another parent going through the same as you at the moment! 
I'm sure the appeal experts on here will be along soon to give you some more proffessional advice than I am able to.