Thanks for the additional facts. So pleased to hear how well your son has been doing.
I do think you should write to the head with the new information. ("I thought I should write and let you know about the following in case there is any impact on my son's work. During the summer holidays, ....................") Keep a copy of the letter.
There is no such thing as "appeal margins". It is true that the majority of successful appeals are for scores in the range 117-120, but lower scores will receive serious consideration, especially where there is a strong case.
For more information about appeals, have a look at:
http://www.elevenplusexams.co.uk/11plus ... nswers.php
Please ask if any further help is needed.