There is a saying that the best things in life are free. Facebook is free, Spotify, libraries the next word in this should be college. Your administration has made efforts to incentivize institutions that make school more affordable. This has been a noble effort but clearly isn't working fast enough.
This might sound arduous but past Presidencies didn't let difficult legislation stop them from achieving meaningful change. A few I can think of is the Great Society legislation, Social Security, making it to the moon and your own Affordable care act legislation.
College would be free for all students seeking to go. Doesn't matter if the school is private or public. Making college free will enable a more competitive and educated workforce and we'll continue being City upon a hill.