I strongly encourage you to look closely at colleges that only require a FAFSA for financial aid, given the non custodial parent situation. Even though they might not meet 100% of need, the net price might be lower than schools that meet full need, but require the CSS. Run the NPC on some of the schools and see if any are affordable.
Some of the LACs on our list that I believe are FAFSA only that you may want to take a look at include (includes female only schools):
Agnes Scott, Augustana College, Allegheny, College of St. Benedict, Earlham, Hendrix, Juanita, Luther, Marlboro, Southwestern University, St. Mary’s College - Indiana, St. Mary’s College of Maryland, University of Minnesota Morris.
I am sure there are others worth looking at as well.