As a parent with 3 kids, two teenagers and one in elementary school, people need to stop being so obsessed with this rankings. They mean almost nothing in the long run. One of the factors in those rankings are the standardized tests. Well you know what most kids know those tests mean nothing to them. They don't impact their marks at all. When my oldest 2 we writing them tons of kids would comment about how they didn't try at all when writing them. One kid joked how he purposely answered things wrong.
Parents need to ignore these stupod ratings and instead go and see the school for yourself. Meet teachers and the principal and talk to parents who have kids that actually go to that school.
Honestly if your just looking at ratings then you are being what some of us refer to as "school snobs". Your child will not get any further in life just because they went to a higher ranked school. In addition, sending them to a different school means they won't get to know the kids around where they live.
Funnier thing is I bet the school you want and the home school probably feed the same high school. So the kids all end up at the same place anyways.