If finances matter, note while D3 do not give athletic scholarships, my kid was an athletic recruit to RPI. They gave him more merit than I would have expected, and have leverage getting qualified students in the door. Note they have top notch athletic facilities and have been great academically for my kid. And it is one of the few that will allow you to go with RD if recruited (at least in another sport but I think it’s school policy).
He had interest from Caltech and a couple of ivies, but RPI worked out well for him. Caltech is a long shot. They really dont care how their teams perform, not even a little, some record setting losing streaks were set in multiple sports. So coaches have little influence in admissions. More in ivies, but as you said, the competition both athletically and academically is fierce at those schools.