I would be extremely wary of going for an indie or a selective school for a child with ADHD - especially if you are only in Y3 now.
It tends to get a lot more problematic later on - and very few indies or selective schools will want the hassle.
DD (Y10) has ADHD and dyslexia. She aces VR and NVR and has 9 & 8s as her GCSE target grades but her actual achievement is way below her CAT test results due to predominantly the ADHD issues.
She's primarily ADD - behaviour is angelic at school (not so much at home) - and has major issues with focus, executive function, organisation. It's manageable with subjects she likes, but the ones she doesn't are just a disaster.
I would find a school that is accepting of SEN and will work with your child's strengths and weaknesses.
Regarding the 4 hours a week tuition... depends on the child. Mine has always been into music and was probably doing that many hours or more from Y3 - and loved it. She's planning on a career in that area and does a crazy amount of hours now.
If your child just happens to like doing 11+ tests (I was that kind of kid) then crack on. However, if you are doing that much in the hopes of getting them a place, be very careful what you wish for.
DD's ADHD started getting a lot worse in Y6 - but we couldn't get a Dx due to Covid. Finally did it this year once we could get all the assessments done properly, and medication has been a massive success so far. Wish I had done it in Y5 when I first started talking to Primary about it.
Watch out for dyslexia and dyscalculia as well - around 70% of children with ADHD seem to have the double whammy.