Your main point will carry more weight if there is some proof. I would not be looking for a report from a secondary school history teacher (it might lead to some doubts - could this be someone you know privately?). I would like to see a supportive letter from the primary school, and ideally mention of the fact that your son pursues this interest in his spare time. No need to go into detail in the written submission, but be prepared to do so at the hearing. I would like to know what (relevant) television programmes he watches. There ought to be time for him to develop an interest in Egyptology and to fit in a visit to the British Museum as well!
I do not think you should make an issue of not having a school place. I'm afraid it's not their problem. You should be focusing solely on why you want a place at this particular school. Of course, if you are asked about your situation, you can reply accordingly - but you don't want to sound desperate and turn it into one of your grounds for appeal.
The other grounds for appeal are the usual: feeder school, good pastoral care for sensitive child, easier to walk to etc. But these appear to be arguments common to most appeals
I think you're right, although the feeder school argument is certainly a valid point (even if it's open to lots of other parents too). If you actually have some sort of proof that your son is very sensitive, then you can legitimately link that with the school's reputation for pastoral care.
With a 10% success rate for appeals, it won't be easy - but you seem very realistic. Please don't hesitate to come back if I can be of any further help.