I will leave the FA discussion to other posters- who are VERY wise in this area, so OP you are in good hands.
A couple of thoughts though about “Business”-
1- He does not need to major in Business, and therefore, does not need to eliminate schools he’s excited about which are affordable just because they don’t have a Business school or major. Down the road he can get an MBA if he’s so inclined (especially if he’s working for an employer who will pay for it) with any major. I was a Classics major- and ended up in what was then a top 5 MBA program for what it’s worth.
2- If he’s numerically inclined and is interested in public health, health policy, any of that nature, a statistics major will make him HIGHLY marketable across a wide range of fields (and gives him flexibility to do something else entirely if he decides to take a different route.
3- There are some really good 1 year or 1 year plus Master’s and certificate programs in data analysis, again- great prospects in health, but lots of other options as well. And a much shorter route to a well paying career than med school!!!
4-Do some serious thought on taking out of your 401K/IRA. Your kid can always get a loan for college (even if you don’t want him to borrow and that’s not the plan right now). NOBODY is lending you money for your retirement- nobody. The current limits- 27K in total for four years of college- mean that a kid who knows how to live frugally (which sounds like your kid) AND can get a job after college, can pay back the loan without living in a cardboard box.
5-Give Rice another look if it might be affordable. I have never heard comments like the one you posted about fit- and I think the college system does a great job of building connectivity and community among kids who might not ever meet on another college campus.
Your kids sound great!