I can’t suggest schools by names, but I can share our ds’s story. Our budget for our kids is smaller than yours, so all of our children have actively sought merit scholarships.
Our ds who wanted to pursue physics/cosmology interviewed the depts at every school he was interested in. He selected the schools by looking over their 4 yr plans, frequency of course offerings, compared textbooks used with texts used at other schools, access to grad level courses, and access to UG research. When he met with the depts, he asked specifically about what types of research their UGs were doing. Who did the UGs work for, profs or grad students? What did the graduates from their dept do after UG?
The dept visits were quite revealing. During one meeting with a dept dean and UG advisor, for example, when asked what students from their dept did after graduation, they looked at each other with blank stares and neither could say what one single student was now doing. (Ironically, that school had been at the top of his list. He ran the other direction.) Another one of his original top choices told him that he had more direct research experience as a high school student than their UGs bc their research focus was on their grad students. (Our ds was accelerated and worked with a prof where he DEed and had attended multiple physics summer research camps.) That school also came off of his list.
The school he ultimately decided to attend is by no means a physics powerhouse nor is it even a top ranked U. What it offered him was access to courses he wanted to take, ability to participate in UG research directly with mentoring professors, and be surrounded by supportive faculty. (The idea that only small LACs have supportive faculty is a myth. All of my kids have attended public Us and all of them have had faculty truly interested in mentoring them.) He was part of a small research-focused honors program and attended on full scholarship.
His UG yrs were focused. He spent about 18 hrs a week doing research. He did multiple poster presentations. He participated in REUs. He took several grad level courses. He maintained a 4.0. When he graduated from that school, he was a strong applicant for grad school. He had great options to choose from and is now a grad student at his top choice.