If it’s a reach, it’s unlikely to meet full need. . .
Unless it’s an Ivy or Little Ivy type school, to which you don’t have the numbers for admission. Schools give their big merit awards to incoming students who are at the top of their admitted class. Obviously those kinds of schools are not reaches for you.
SUNY Geneseo should be your gold standard because it offers an excellent program at a well regarded school with a cost at less than $30k before they even look at any additional financial aid.
With the standard federally guaranteed student loan, your family’s cost should be down to about $24K. And that’s before w’ve even talked about money which you should be able to earn with wor’ study or a job on campus, which realistically could be about $9000 @ 20 hours per week with NY’s minimum wage. That brings your family’s cost down $15K. Obviously you need spending money and money to buy books. That’s what summer jobs are for.
The bottom line is that Geneseo is eminently affordable and. You shouldn’t even consider another school unless they can come in at a lower cost than that, given your family’s circumstances. For most applicants, their state school is the standard, but PA is so bad at supporting their state universities that it’s not in your case. But you’re fortunate that a state right next door to you offers such a good deal.