I will not qualify for any need-based aid. What is my best plan of action to help out my parents?

No matter what schools are on the radar, I would want to drill down on what “pay for” means to OP’s parents.

This would be an early step at our house, before we put lots of time and $$ into multiple elite school apps. That being said, with your stats I’d still want at least a couple of ‘elites’ on the table. But having the $$ discussion would help me to narrow or expand the field.