To be competitive at the privates, you need really high SAT’s. Your 2000 is probably a little weak for the ones that will give you money. USC would not bend over backwards to give you funding with that score.
Also, a lot of the privates are religious-based, so you have to make sure you check online what kind of requirements they have.
(ex: on the west coast: Chapman, Pepperdine, USD, have money, but they are backed by certain churches.)