Back to your $15K. Is that what you want to spend or two the financial aid calculators tell you that’s all you can afford.
Go on a top tier school like Cornell - enter your stats and see what your net price is.
If you can afford $75K but only want to pay $15K, then the chain above is valid. If you want to pay $15K and they agree you can only afford $15K, a whole new world opens up.