Our kids have the same age spread as yours. We started thinking about making the move at the same time as you. That was also the time when our older child was performing above grade level at his public. Unfortunately, that checked the box for the school. The teachers only had time for the kids who couldn’t read and had behavior problems. He was deflated after the day. We moved him into the new school two years later (kept him in public during the pandemic). He blossomed at the new school. We saved the next two years so we could send our other kid as soon as we could afford it. I don’t know if we would have had the same luck getting in had we waited past elementary. Not all schools are the same, but my sense from the school/parents/admin is it gets harder every year and the older the kids get. But if they have a strong sibling policy, it should be easier for the other sibling if you’re an existing family.

If you can afford it, apply early. Depending on the school, entering in middle school could be hard socially. And the longer you wait, your kid will be competing with every other kid whose parents chose to save money for elementary school. When people say "return on investment"....I laugh. Private school in an investment in your child. As parents, we invest a lot in our children with no expectation of a personal return. And if you are sending them to private school as though it will get them an Ivy League spot without them having to earn it, then of course - save the cash and send them down the street to the local school.