As a Business major (you can declare Finance later), I would swap SMU over Tulane if you want to add a private school. I would also suggest you add Arkansas, as it is stronger than LSU. Second the other posts about adding Indiana. Since you live in TX, I would have a compelling reason for leaving TX or a border state. Most of the border state schools have OOS merit for TX applicants. Travel time and weather will be a hassle the farther you drift from DFW.
Make sure you keep your rank in that top quartile.
If you consider the economics route I would be sure to take the time to compare the curriculum of an econ major (a liberal arts major) to that of being in an undergrad b-school program. There should be information online. One path is not better than the other, but there will be a notable difference in coursework.
Would business courses be easily available to non majors? The business major may be more selective because of capacity limitations on business courses, so there may be little or no space for non majors in business courses.
However, economics departments may have their own financial economics courses. But note that economics as a major has significant differences from business as a major.
McCombs has business programs for non-McCombs students. They specifically have a finance minor for economics students. I don’t know how selective it is to get that minor but it looks like anyone who qualifies can do it…not sure…just guessing that from the website. OP is HIGHLY qualified but just not likely to get McCombs as a major due to both his rank and the fact that even top 5 percent-ers still often don’t get it. The finance minor for Econ majors is definitely an option to consider. And I would say UT College of Arts and Sciences/Econ Major is a low target (good shot at admission) for OP.
Honestly in-state College of Liberal Arts is a target for MOST students in the top half of their class from a competitive school. If OP tanks junior year then it might not be a target. But given where they are now that seems unlikely.