If they have $30,000 for you, then that means only $7,500 per year at most. Adding federal direct loan ($5,500 in the first year) and some work earnings (perhaps up to $5,000 per year at most is a realistic expectation) puts your outer limit at about $18,000 per year (but cheaper is better in case you cannot work as much or some of the $30,000 gets pulled for a family budget emergency).
Since the merit at the unnamed state university is not assured for stats, you probably want to find a safety where the merit scholarships that bring the price within range are assured for your stats.
Tulane has both early action and single choice early action, as described at http://admission.tulane.edu/apply/instructions/ . Single choice early action means agreeing not to apply early action or early decision at other schools (with some exceptions for state schools as listed), and signals a higher level of interest in Tulane (which Tulane does consider in admissions, a concern if your stats are much higher than typical Tulane frosh, so that it looks like you may be applying there as a low choice “safety”).