You wrote this: “Schools do not say they are need aware…”
I replied saying this statement is not true.
Here is some support for my position:
Colby aid packages contain grants and work-study aid—but not loans. While our admissions process is need-aware…
https://www.colby.edu/admission/admissions-and-financial-aid-requirements/
Need Aware/Sensitive and Meets Full Need: All admitted students will receive a financial aid package that makes attendance affordable, but some otherwise qualified students may be denied if the institution cannot afford to offer the aid they need. This is the scenario at Tufts and many of our peer institutions.
Smith meets the full documented need, as determined by college policy, of all admitted students who apply for aid by the published deadlines. Because Smith follows “need-aware” policies, a small fraction of admission decisions may include an assessment of the student’s level of need.
https://www.smith.edu/admission-aid/criteria
While not all schools that are need-aware publicly state that they are (at least not in a clear way that is relatively easy to find), the examples above show that there are need-aware schools that do indeed say they are need-aware.