A lot of the full-need-met DIII schools have very traditional liberal arts curricula where you will not find majors like business; however, plenty of students from schools like Williams, Amherst, Pomona, Vassar, etc. still end up with business careers. More full-need-met options in this category: Connecticut College, Hamilton, Skidmore, Middlebury, Wesleyan, Colby, Bowdoin, Bates, Swarthmore, Haverford, Carleton, St. Olaf, Macalester, Colorado College, Kenyon, Grinnell, Washington & Lee, Franklin & Marshall, Gettysburg, Dickinson, Pitzer, Occidental.
At the other end of the spectrum (but still DIII and meeting full need), consider Babson, which is a unique and top-tier school with a business/entrepreneurship focus. They don’t have traditional “majors,” but rather a core curriculum plus a wide variety of “concentrations” which are more like minors. It’s a one-of-a-kind school - worth a look to see if it appeals.
Then there are the mid-sized DIII universities: UChicago, Tufts, URochester, CWRU, Carnegie Mellon, Johns Hopkins, Emory, WashU in St Louis… and then there’s NYU, which is larger and probably has some of the attributes you like about USC (minus the California weather, but then again NYU Stern is a bigger name for undergrad business than USC Marshall) but is DIII for sports unlike USC.
And lastly there’s Claremont McKenna which might really hit the sweet spot for you. It’s a tippy-top school for poli sci, econ, and IR, with a strong business/pre-professional bent. Small, but part of a consortium with 7000 undergrads and seamless cross-registration. (Two athletic programs: Pomona/Pitzer and CMC/Mudd/Scripps) Full need met aid, great weather, and the top men’s DIII soccer team in its region. The other DIII full-need-met LAC that has a bit of the same kind of pre-professional leaning with strong Global Commerce and Politics & Public Affairs majors is Denison in Ohio - could be worth a look as well.
One question is whether you’re willing to join a lower-ranked DIII team at a school that is top-tier academically. Some schools obviously wouldn’t require that compromise (Tufts, Amherst, CMC, Swarthmore, UChicago for example) but others are stronger academically than athletically and might really want you as a player. For example, NYU and Carnegie Mellon both have T10 undergrad business programs and DIII soccer teams, but they’re not at the top of their leagues athletically. (Whether this means they’d want you more, or whether they’re not powerhouse teams because they don’t recruit as hard, is for people who know athletic recruiting better than I to say!)