Apply to FAFSA only schools. My son had to do the same thing. Although his dad does not make a huge amount of money, it’s enough that it would have been highly detrimental to any aid and he wasn’t going to help pay for school (couldn’t really, he has medical issues, two young children at home as is the sole earner).
There are plenty of great schools that aren’t the private elite and if you can get into one of those top schools you’d probably qualify for merit as well as need based aid at ones a tier down. Here’s a complete list of all schools that require CSS and what they require, just filter out the ones that require CSS for the non-custodial parent (not all do).
https://profile.collegeboard.org/profile/ppi/participatingInstitutions.aspx