Hi and welcome
Unfortunately I don't think the sibling link and travel will carry any weight at an appeal.
I just feel that his maths result does not reflect his maths ability.
I think that this bit is the key really, if you can prove that he has very good maths skills with lots of evidence: level 5a or perhaps even level 6 predictions, good CAT scores for maths and perhaps additional support in maths for G&T with good HT support then maybe an appeal for Judd is do-able.
Being kind to your son though, perhaps it is a long shot and you should perhaps prepare your son for a place at TWGSB or somewhere else, rather than keep hanging on for 5 or 6 months until the appeals are over. Over 400 is such a good score and its sad to have worked so hard and be disappointed, maybe focussing on the schools he can get into would be an idea. You could do an appeal without his knowledge if you wanted.