I took a look at CollegeBoard’s list of schools that require CSS Profile, but not NCP financials for 20/21. https://profile.collegeboard.org/profile/ppi/participatingInstitutions.aspx
Other selective schools (a step or more down from U Chicago and Vandy but still good/very good schools) that require CSS Profile but don’t require NCP financials are:
William and Mary
College of Wooster
DePauw
Elon
Gettysburg
Lewis and Clark
Oberlin
Providence
RPI
Santa Clara
Stevens Institute of Technology
Do double check this info on each school’s site.