Usually highly rated private schools have built in college counseling. Often times the 30% rank at a private might get into a top top school whereas maybe not at a public - depending on the school of course.
Because the school is private, they might have a better idea of where kids end up so might be able to match you statistically.
If you want large schools - which you’ve chosen other than Duke, you might consider UMD and Va Tech.
But given the folks are at Duke, if you decide you like that size, a Vandy, Emory, Rice, WUSTL etc would be great. Emory has a Quant Sciences major you might like - you have to dual with another.
But Pitt and NC State are great and I think safe.
I just think your counselors might be a better guide in this case.