You might add leigh, clarkson and university of rochester to the list. Stony brook also has honors college. Select accepted students are invited to join. Colorado school of mines does offer some full tuition merit scholarships. You cant apply directly. Select admitted students are invited to apply. My son made that cut but not the final one. The school was on his shortlist but he opted for elsewhere. I’d suggest going on a couple of informal tours at 2 or 3 colleges over the summer to get a feel for size, programs, etc. Out of state university of illinois-champagne urbana is strong. University of pittsburgh has rep of good merit $$$. Youre smart to at least start thinking about things now. Good luck.