I am sorry that your Head isn't supporting you because of "political reasons". Tell the appeal panel that when you meet them - they may well have come across other parents from the same school, and be familiar with the problem. (I wouldn't put it in the appeal letter though.)
Your appeal letter should be kept very brief - one side of A4 if possible. Any other evidence should be submitted as numbered appendices. These might include short written statements from the class teacher, or teachers of core subjects and copies of pages from school reports (core subjects only). Any statement of special needs/Ed Psych report should also be sent in advance to give the panel the chance to understand the issues fully. If the child has, for example, won a County Chess championship or a scientific award, then a newspaper cutting would be appropriate. For other extra-curricular achievements only something really major would be worth putting in - a sporting 1st place at county/national level. A snap of little Johnny in the back row of the chorus at last year's panto will not cut any ice! Nor will letters from Brown Owl, saying what a good girl little Jane is each week at Brownies!
The panel will have literally a couple of minutes to look at school work, and what they will most want to see is English/Maths/Science exercise books. If there is an exceptional piece of project work for one of the core subjects, then take that along. Just be very careful not to over-face the panel - you will not be thanked for taking in great volumes of paper, and it will just obscure the very best work if you do so.
You do not need to submit all the evidence with the appeals letter - you can submit further evidence by post up to 7 days before the appeal (don't forget the Christmas postal delay!) or even, in extremis, take it with you on the day.
Also, remember that your appeal might be heard before the start of the spring term, so make sure that you have any evidence you need from the school before the end of this term.