Gruach: "An enjoyment of challenge and an ability not to get bogged down by stress."
I think the above is essential. We applied to a range of schools in terms of academic rigour and hoped that at least one would be a good fit for DD. Over time, it became clearer to us that DD was drawn to an academic setting. How did we know? I suppose it was little things like DD becoming engrossed grappling with challenging problems and her eyes lighting up when she figured out something that had previously flummoxed her.
As for "shining", I believe it was SPGS's head mistress (or this year's head girl) who told us that girls who need to be "No. 1" will be less happy there. Rather, girls more likely to enjoy SPGS are those who get excited being surrounded by bright and talented peers. It is a positive that the school does not rank the girls and it appears that most girls will have an area or two where they "shine" and others where they are more or less average relative to SPGS peers. Our DD is not competitive by nature and seems to get a kick from hearing interesting thoughts/ideas from schoolmates - so, hopefully she will find SPGS enjoyable.
DD loves to read (including books that are intended for children a few years older) but that doesn't mean she understands everything. In fact, we noticed that the subtleties in 11+ English passages often escaped DD (she is also a summer born) but decided not to do much about it because it simply reflected her level of maturity at that time. (By the way, my hunch is that perhaps this area is where SPGS may adjust for differences in age.)
Lastly, children's intellectual capacity can take a huge leap around age 9-10. With DD, the strides she made in some areas over this period really surprised me (I would imagine many parents have had similar experiences) - for example, on some maths concepts, DD went from having difficulties grasping the basic idea to devising her own problem-solving approaches. I guess it is matter of her brain becoming ready to engage in more complex processing. So, the end of Y4 may be too early to rule out SPGS (I remember thinking when I first looked at the SPGS practice papers - at the start of DD's Y5, I believe - that there was no way she could pass them).
Alto, I hope the posts on this and other threads can help you (and others similarly situated) make an informed decision. Good luck!