My (hard earned) opinion on public vs private vs whatever is ultimately it comes down to admin + teachers + standards, and in no school do you get to choose your admin or teachers or standards (you get what you get and you don't get upset.)
So if you can, my advice is to leave yourself as much budget and time to teach your kids yourself or supplement with instruction you choose to fill in gaps, because no matter what: you will find gaps. They will maybe show up every year, or be bigger one year than the other. These are human systems with human problems--you have to be the net.
I've ultimately found that our kids academic performance is a reflection of our family values, how we spend our time, and what we expect from the kids. School can support or accelerate it, but at the end of the day we hold the job as parents.
Lucky to have the time and resources to do it, so we make it a priority. This has been something
@elawless has built into our family system, and I'm deeply grateful.