Welcome to the forum!
Will I be able to find out if she would have got a place with her score on the first round of applications, in which case would I structure the appeal around the circumstances that caused the late application?
Although you cannot argue that there has been an error in the admission arrangements, you do need to explain to the panel the circumstances around the late application.
I suggest you acknowledge that the LA and school were very sympathetic, but acted correctly.
(It's more likely to win you some sympathy from the panel!)
Or should I focus on oversubscription and why that particular school is right for my daughter.
Yes!http://www.elevenplusexams.co.uk/appeal ... -school#c2
My other possibility is that she also does around 20 hours of sports training per week outside of school hours (she competes at national level), and achieved her test result despite this and with no tutoring, so we could explore this to demonstrate academic ability.
I wouldn't advocate this line of argument as her ability isn't really in question.
You cannot, in any case, prove a negative (i.e. that she wasn't tutored.)