Very few schools “meet need”; there are only about 60-80 colleges that promise to meet 100%. The others pick and choose who they’re going to “gap” and who they’re going to entice with merit scholarships. The former tend to be those in the bottom 50% for stats, the latter tend to be those in the top 5-10% for stats, and everyone else must hope the NPC results were accurate. The only financial aid everyone’s sure of if the fereal loans for 5.5K a year.
You have them here:
http://www.thecollegesolution.com/colleges-that-meet-100-of-financial-need/
http://www.usnews.com/education/best-colleges/paying-for-college/articles/2014/09/15/colleges-and-universities-that-claim-to-meet-full-financial-need?int=970708&int=970708
Note that for public universities “meets demonstrated need” is to be understood "for in-state applicants).
Run the NPC on Oneonta (and look into the program with FIT) as well as Marist.
Check out the scholarships at Miami-Ohio and UAlabama, which sound like they’d be good fits, too.