The key to almost every selection appeal is academic evidence, so extenuating circumstances are going to be secondary.
Decisions are going to be based mainly on the evidence that is available. It's my view that all the evidence (both academic + extenuating circumstances) can speak for itself.
I don't attach much importance to the appeal submission. Essentially all it need say is, for example:
Appendix 1: Letter from GP
Appendix 2: Letter from school confirming how my child was affected during the week/month of the tests
By all means 'top and tail' it: "Dear members of the panel ...................... Thank you very much for taking the time to consider our appeal.
I would keep the presentation quite brief, and suggest its purpose is just to remind the panel what your case is all about and to highlight the main
points in the evidence
If the panel want or need to know more, let them draw the information out of you during the Q&A session.
That would be my ideal appeal.