I agree it depends where you are and that actually, moving at Year 3 is a good time to move - as pp said, there is no 11+ preparation (as such) in Year 4 so your DS will be able to settle, but in my view, the earlier the better.
I do disagree slightly however that schools won't offer anything more if they're in catchment (other than parents being aware of the entrance exams). Where we are, it is an expensive area that people choose to live in simply for the schools. So there is an expectation, from parents and from teachers, that passing the entrance exams is on most parents' agenda. Whilst the schools are not supposed to coach, there is work that is definitely aligned to the types of questions that will be asked in the entrance exams, and most importantly at our school, most (if not all children) are working a school year ahead for maths. So my DC covered a large chunk of the Y6 syllabus for Maths in Y5, so when they took the entrance exams at the beginning of September in Y6, with "stretching" maths questions, they were able to tackle those questions relatively easily.
I would also suggest that if you're moving into a grammar school area and are going to use a private tutor, you need to sort that out well in advance.