What an incredibly interesting son you have! I think it will take several of us to produce an adequate response to your question, so let me start with what I can contribute.
I understand fully the problem with your child's brain not working in the way that the tests require. My own son is similar, being very strong at Science and Maths, albeit he is far less advanced academically than yours. There is limited evidence available that a small minority of children are so "left brained" that their brains work in a way that is diametrically opposed to the skills needed for Verbal Reasoning, and that would skew an 11+ plus result by three marks without difficulty. Unfortunately I cannot provide any direct links to the information, as I picked it up mainly from websites about dyscalculia - children with dyscalculia have very strong VR skills.
It seems an odd suggestion, given how bright your son clearly is, but have you had an Ed Psych report done on your son? That could highlight the exact reason for your son missing the 11+. Even a chat with an Ed Psych could give you the information I am referring to.
I would like to think that even the most obtuse Appeal panel would realise that your son is a huge exception to the normal rules. However, I think you would be very wise to emphasise your last point - that you want him to develop as a normal child, as that should allay any suspicions of you being a hugely pushy parent.
Also, if the system in Kent is the same as in Bucks, the Appeal hearing is about entitlement to a Grammar School place, not about a specific school, so you should mention the dilemma on the alternative schools as "follow-up" evidence, rather than as the main thrust of your appeal.
Now it is over to others to offer what they can...