This will likely cause you to overlook some good schools that may offer sizable discounts, and that’s what many schools are doing…discounting. I’m not talking about the ones that have merit grids based on GPA/test scores because those are the ones where merit is more likely to be on the NPC.
Schools that are discounting often don’t show this on the NPC because it can vary dramatically from year to year…schools offer bigger discounts to students they most want and that can be relative to that year’s applicant pool. Sometimes a larger merit/discount is based on stats, sometimes not.
The CDS are your best source to research non-need based aid at each school. This is a good resource that attempts to aggregate this CDS info and you can sort how you want: Release Domestic Financial Aid 2021 - Google Sheets