Maybe athletic recruitment would cancel out the low-EFC disadvantage? Big question is, as you say, whether NPC results are favorable enough in the first place. If they are, then CMU is the one full-need-met DIII university with a highly-ranked quant-heavy undergrad business program - peer to UVA and Chapel Hill - if that’s something OP wants. OTOH, if he wants more of a pure-academic poli sci, econ, or PPE* type program, there are probably better options than CMU.
OP, there are a number of schools that offer “PPE” - Philosophy, Politics, and Economics - as an interdisciplinary major, often a seminar-style honors program, modeled after Oxford. CMC has this: Philosophy, Politics and Economics (PPE) - Claremont McKenna College - Acalog ACMS™ as do Pomona Philosophy, Politics and Economics Program | Pomona College in Claremont, California - Pomona College and Denison Philosophy, Politics & Economics | Denison University Denison also has a particularly strong semester-in-DC program.