Save for you retirement first. That will not be counted on a means test and some 403 B's let you borrow against it...but this is a last resort.
Make your child scholarship worthy. When my daughter expressed an interest in band, I encouraged it because many instruments are 'scholarship' instruments. Kids don't take them up an so top flight universities are anxious to get kids that play these instruments. The kids don't have to major in music, just perform in x number of chamber groups and the university band or orchestra. My daughter played the oboe (sax, keyboard, and several others). Her musical ability got her into the best high school in the city (audition admission). This in turn lead to a top notch university on the West coast. They under wrote much of the cost. she still has some to pay, but not as burdensome as most. There are scholarships in swimming that go unused while many fight over the few football scholarships available.
Treat the search for money like a part-time job. Fill out forms and write essays until you get cramps in your fingers. The money is out there.