<p>The only publics that could be on your list that are out of state are UVA and UNC which you think are too selective so public schools OOS aren’t on your list. The schools that I mentioned are literally the only colleges that qualify under your criteria. No OOS public schools exist that are better than UW-Madison that would meet need that aren’t UNC or UVA hence why I suggested private colleges (Few of these also exist because you want a large school with a marching band.)</p>