Essay might be not the key in your D20's case

The public HS, which is not in the radar of top-elite schools, might be;

AO might not seriously go through applcantions from your public HS due to the large number of applications from HSs which are in their radar;

I was posting the suggestion of applying for small top LAC. They likely seriously evaluate highly competitive applications from your public HS due to the relative small number of applications especially in ED I/EDII.

Anyway, flagship state college is also a great place to learn and grow.