Nobles has about 50 boarders, or about 10% of 9-12 kids, and it’s only a 5 day option. It’s a very sports-oriented school, and that is not obvious in your ECs.
It almost feels like you cut and pasted the Niche Rankings for schools you wish to apply to, instead of doing real research on schools that may be a fit.
NJ/PA/DE has many solid boarding school options - Peddie, Hill, Mercersburg, Blair, St. Andrew’s among them, each with a multitude of offerings in economics and politics.
Lastly, it’s your parents’ money, not yours:
Your quote: “I currently go to an extremely good school which is somewhat of an Ivy feeder in it’s own right. So if I’m going to spend and extra year in high school, and an extra $100,000; it’d better be at a school that’s way better than now”.