To echo @vegas1, most schools have a FA pool for middle class students. This is often a challenging demographic for BS…
Many middle class parents assume they won’t be eligible, live where they have decent public schools (and have funds to augment their kids’ experiences, whether academic, athletic, arts, etc), and are keeping their powder dry for college. The upshot is that most BS tend to get lots of applications from wealthy families and lots from families with full (or close to it) need because they really need an option that’s not available locally. Notably absent are the kids from the middle.
It’s good that you are expanding your search, but I mention this so you don’t despair!