OP my DS (also very bright, think 120 maths SATS) did not get into a selective grammar initially (he was nervous in exam) though his equal ability twin did and is flourishing.
The twin who didn't get in went to comp in Sept. About a week into term he was offered another place at a selective grammar, which he declined as he was initially happy at comp. I had my concerns on here as Noble and others may recall as I was concerned that by one twin at grammar and one at comp, differences may arise.
Several months in and my son (and us) would give anything to have the grammar place back. He's not happy at school and the differences in confidence in learning between the gs and comp is growing. DS at grammar is flourishing, loving learning in a great environment.
DS at comp is in all top sets but low level disruption, some bullying for being bright and teachers don't really bother with him. He's uninspired and has to wait for others to 'catch up'
This is just our story. My brother was a maths whizz, went to that same comp (was bullied for being bright) ended up with a first in Physics from a RG uni and has a fantastic career so every case is different.
However, if I were in your shoes, If I could turn back the clock I would have grabbed opportunity.
We are looking into independent schools ourselves now.
My DS did not 'perform' as well as expected in the 11 plus (even though he did eventually get a place offered) He's far better in class. So I see your point about entrance exams - they can damage confidence if you are not careful.
Good luck.