I realize you’re talking about Los Angeles…but there’s another LA…Louisiana, the birthplace of jazz!
Loyola New Orleans’ jazz studies program is well thought of. Additionally, Loyola tends to be very generous with merit aid.
University of New Orleans is a public school with another jazz program and public school tuition tends to be pretty reasonable in the state. They’ve had some enrollment/financial issues the last few years, but will be going into the LSU system next year which is expected to help them right the ship and grow in the right direction again.