You might also consider colleges in the area like Seton Hall and St. John’s University. The Catholic schools may like your story of change, the SAT score sits squarely in their wheelhouse, and Seton Hall in particular has a good business program (I’m not as familiar with St. John’s program). Seton Hall likes demonstrated interest, so if you attend their open house soon then you can show some interest, get your app in quickly, and hopefully get a relatively quick decision as they’re rolling.
Also, I think you have WAY more choices than you might think. Smaller colleges, especially ones in the NY/NJ area might work well for you.