Wow - Tulane reall has decreased their enrollment.
That is good news for the school - it had too many students.
You have time to visit the schools, and that is more important than talk about connections and other stuff IMO. All that stuff really does work itself out. My advice is don;t worry about it too much. Visit the schools, pick the one you like the most and stop thinking about it. You really can't go wrong with any of the 3.