I have sent the details to the appeals box - and look forward to your comments
On the whole the decision letter is better than average!
It appears to meet legal requirements - although it doesn't state whether the admission arrangements (including the area’s co-ordinated admission arrangements) complied with the mandatory requirements of the School Admissions Code and Part 3 of the School Standards and Framework Act 1998.
This latter point is something of a technicality (in that it doesn't mean you've suffered an injustice).
It's reassuring that the panel questioned the school case. (We hear too often of panels that don't ask a single question and appear to be 'nodding through' the school's case!)
The number of questions asked in relation to your case wouldn't be grounds for a complaint.
The chair does have a duty to manage the time effectively, although this must be balanced against the need to allow you to state your case fully and answer questions.
It's not clear to me whether you were asked at the end if you'd had sufficient time to say everything you wanted to. (This would have been good practice, but strictly speaking isn't a requirement.)
The length of the hearing appears quite reasonable.
It's customary for a decision letter to reflect very briefly the key points raised. Of the three points you mention, the first two are covered to some extent. The allocated school isn't referred to, but the omission could probably be justified on the basis that this is an appeal for
a school, not an appeal against another school.
I'm afraid I see no grounds for a complaint at the moment.
If you were able to get hold of the clerk's notes, I don't mind checking them for any procedural errors. I think you'd be entitled to a copy - but be warned that they may resist!http://www.elevenplusexams.co.uk/appeals/ombudsman#d4
I do sympathise with regard to the outcome, especially as you succeeded in overcoming the first 'hurdle'. In my experience the sort of case you have is usually quite compelling at the prejudice stage.
Unfortunately it's not possible to challenge the panel's judgement.