If you think you can “figure out how to be full pay” and are worried it will hurt to apply for FA. Maybe just go ahead and do that? I think if you can figure out a way to get the money, then maybe the SSS will also tell you to do that.
Middle class families can qualify for more than 50%, and schools will give it. Agree that schools need a middle class, or they would be in a weird place with a student body consisting of the upper 2% and lower 10%. And most middle class families don’t have a spare 30-65k sitting around. Trust the process.