If your budget is 30-40% of the full cost of a private LAC, that would be about a 30K budget, correct?
You may want to look at some of the public LAC’s where you could afford to full-pay. The most affordable ones - definitely under 30K/year - are University of Minnesota, Morris, and Truman State University in Missouri. Both are fine schools that send many students on to top grad programs, and your son’s ability to attend would not be dependent on financial aid. He would get automatic merit at Truman State, reducing the cost even more. Admissions are rolling at both; Morris has a Dec 15th priority deadline for maximum scholarship consideration.
Somewhat more expensive but still likely affordable public LAC’s include SUNY Geneseo and UNC Asheville. Both of these have Nov 15th Early Action deadlines.