I've had a careful look at the correspondence, and my personal opinion is that there has been maladministration.
If, by any chance, the EFA were not to find in your favour, I would suggest taking the matter to the DfE.
The key point is that the panel appears to have acted incorrectly by applying an additional test in its decision making.
I have to say that there was a similar case earlier this year (though not relating to an academy). The ombudsman ruled that the panel had acted improperly because, having agreed that the child was of grammar school standard, it was not then open to them to go on to consider how the child would 'cope'. Having agreed that the child was of grammar school standard, the only legitimate remaining issue for the panel was whether the parents' reasons for wanting a place outweighed the prejudice to the school.
I was also concerned to note the phrase "considerable additional support from the teaching staff". There is an implication here that the panel may have been considering the prejudice that would be caused to the school by the admission of this particular child. I believe that this would be contrary to the ruling given in The Court of Appeal with regard to R (M) v Haringey Independent Appeal Panel & Secretary of State for Children, Schools and Families . As I understand it, any decision on prejudice should be "essentially objective" - in other words, the issue should normally be the prejudice that would arise from the admission of an additional child, rather than this particular child.
I note that the panel considered whether the admission arrangements had been correctly applied, but appear not to have considered whether the arrangements were lawful. This is a breach of the Code, but is likely to be seen as a technicality unless it could be shown that you suffered an injustice as a consequence.
The failure of the school to signpost your right of appeal might also be viewed as a technical error, except that in this instance you can submit that you were disadvantaged as a result.