I agree Applied Math sounds like something worth checking out. Not that he has to commit now, but it might be nice to know it is an option.
A lot of times Applied Math is going to be like a concentration (or just some electives) in a Math major, but I thought it worth mentioning that Stony Brook actually has a legendary Applied Math department (#13 on that Top 50 list, for example), and it is not reachy but still an excellent college:
I believe their full cost OOS is within budget, and then they sometimes toss in some merit.
Another public worth considering would be Pitt. Great location in a fun city, very good Applied Math program, starts just barely on budget but might offer some merit:
I agree Rochester seems worth looking into, but you’ll need some significant merit to get on budget. Still, they do have merit!
Similarly I agree St Olaf might be worth considering as it has a lot of merit and a strong Math program. They are a good example of Applied Math being something you can concentrate on within their Math major (they have something called an Individualized Mathematics Program, and you can make Applied Math an area of emphasis):
https://wp.stolaf.edu/math/the-mathematics-major/
FYI, they are in a smallish college town they share with Carleton, Northfield, but the Twin Cities are only about 45 minutes away.