it was an upsetting time for all of us and he was still not well when they returned to school in September.
I do sympathise, but to be honest, unless there's evidence from the school that your daughter seemed distressed in September, and it can be proved from tests or exercise books that the standard of her work suddenly declined, I can't see either a review panel (which appears to want exceptional reasons), or an appeal panel, giving huge weight to the argument.
Forget the As for effort! High achievement is what matters.
You've already noted that some of your evidence is going to be contradictory.
Nevertheless, your best hope is to think less about the extenuating circumstances, and to focus on compiling the strongest possible academic evidence.
2 x 117 is a respectable start.
I'd like to hear in due course:
the KS2 predictions (preferably 5a/5b level)
+ what level of recommendation your headteacher has given, and whether most other children at the school with the same level of recommendation qualified in the 11+.