Hello I have read your posts, and have to say that sounds absolutely awful, hope you get your son out of their ASAP and find somewhere where he will be able to develop and shine.
I won my secondary school appeal in Birmingham where wining an appeal is considered near enough impossible! So my advice to you is, gather all the bullying incidence reports, emails to the school everything on paper that will provide evidence that this is a common, traumatising occurrence that happens in school.
Secondly, him being your carer is a very important factor and his needs and requirement of pastoral care is vital to cope with his responsibilities at home.
The trick is state your child's needs and match them to what this school can offer to help.
State only the facts about current school offered I.e ofstead report on lack of pastoral care etc. Don't be nasty about the school offered what ever you do.
I think you have a really strong case, what you need to do is prove to the panel that the disadvantage to your child not being admitted into the school far out weighs the disadvantage that would cause the school if they admit your child.
Also, in stage 1, I would try and weaken the school's case as much as possible. I.e have they gone over Pan? If so, find out if the school have achieved good results this will show that they can cope with another child being admitted. If they claim all sorts of havoc will be causes in corridor ask if they have reported any health and safety incidents...chances are probably not!
I wrote a comprehensive statement for my appeal. I found that this helped as the panel knew a lot about us and our situation, if yours is an in year appeal I would advise writing a detailed appeal statement. Most experts advise to write the main points in bullet points..in my experience I'm glad I write a comprehensive statement as I didn't need to stress on so much detail.
Every main point you make, back it up with evidence and match it to what the school offers that the other school can not offer.
I wish you all the best, I'm more than happy to answer any more questions.