Tulane is your best bet based on your criteria but they care about demonstrated interest and the deadline is soon. Tulane is not a safety although applying ED would help greatly. EA or ED is required for merit aid.
You would likely get their $32,000 merit aid based on your stats. If you apply to Deans Honors Scholarship and Paul Tulane I think you would also be competitive and both are full tuition. If you just get the $32,000, your net cost would be just above $30,000/year. Being a dorm RA could reduce that your sophomore year.
But again, Tulane can be fluky on admissions with high stats applicants and DHS and Paul Tulane are involved applications. Early Action deadline is 15 November and DHS/Paul Tulane is 05 December.