The good news is that a lot of the narrowing has been done for you, given the financial parameters. Though your son's test scores make him a contender for the Ivies, super-selective LACs, etc, any school that gives purely or primarily need-based aid and no full-ride merit scholarships isn't going to work, as you saw from the NPCs you ran. It doesn't make any sense to apply to those. There have been good suggestions above about state schools with automatic scholarships like Alabama, and the possibilities open if he makes National Merit.
There are some special-application full-ride scholarships at LACs, though extracurriculars, leadership and essays are important for those. The schools will generally be in the South; here are a couple:
We're homeschoolers and my daughter has taken a number of courses through them. They're inexpensive and easy to work with. Her AP Psych last year had a very reasonable workload and she got a 5 on the exam with very little additional review.
There are so many ways for an applicant to get an idea of the current campus culture; it never occurred to me that the alumni interview could/should be one of them. I think of it as a way for the college to learn more about the student’s personal qualities, and conversely for the student to show those to the college. And while a recent grad might be easier for a candidate to relate to, an older alum, not only parent or grandparent age but an actual parent or grandparent, has the benefit of additional life experience and perspective in understanding the candidate and presenting him or her effectively to the admissions committee.