That can make the search significantly more difficult, particularly for safeties. Assuming a top-end rank, a Texas public university that he qualifies for automatic admission at and does not have additional competition for CS could be a decent safety at in-state prices, but if those are ruled out, finding an affordable safety becomes much more difficult.
Have you tried the net price calculators on various private schools of interest to see if need-based financial aid may work, or if his college search must be merit-scholarship-seeking?
If he does well enough on the 11th grade PSAT to make National Merit Semifinalist and then advances to Finalist, that can open up a much larger set of scholarships based on National Merit status.