Congratulations on a stellar high school career. You would be a strong candidate at any of the schools on your list.
Have you run the Net Price Calculators for each school? I ask because with a family of four income of $160k in NC, and a price target of < $35K, it is unlikely you will qualify for financial aid beyond the $5500 student loan.
To meet your goal, I would suggest that after running the NPCs, you check to see if any of the universities have merit scholarships you may qualify for.
Check out Dickinson College, which offers some very generous merit and has an excellent IR program. Review the list of Catholic universities that offer merit - this would not include the top eight or so, so NOT Georgetown, Holy Cross, Boston College, Notre Dame, but those ranked further down. Fordham is a good idea, but I think you will be hard pressed to end up with a cost of $35k simply because living expenses will be so high in NYC. Catholic Charities is one of the very best refugee resettlement agencies, and attending a Catholic university might offer some interesting opportunities. I’m partial to Jesuit universities, which focus on the whole person (cura personalis).
Finally, what about NC State or UNC Chapel Hill?
Keep us informed of your journey. You are pursuing a noble calling, I wish you all the best.