Great post 2020Hopeful. In my opinion you are thinking along the right lines. With our 2019 we took the advice of a longtime poster here (Wally Lubanski) who advised a few things:
1. Each kid has his own academic/athletic/personality profile and it's best to understand it as early as possible in the game in order to plan accordingly
2. Go where you would want to be if baseball (any sport) weren't part of the picture (4 vs. 40)
3. If sports is part of the picture, go where you will play, BUT even if you don't play, if 1 & 2 have been prioritized correctly, you might be real happy at the end of the bench at one of the top 10 schools in the country
Like your son, academics are before athletics for mine. He is also on the quiet/nerdy side (in the best possible way)! He also knew what he wanted to study (physics/computer science - definitely STEM related). All of that helped narrow his focus to a situation where he will hopefully find his people and thrive primarily academically and personally. Our approach was the same as yours--let baseball get him in a school he really loves & is a great fit FOR HIM, where he might not otherwise get in. Through lots of academic and athletic legwork/trips he found that school in Caltech, where he received significant need based aid (we're not rich, but not poor either).
Now he had other options at very good schools, but not a top 5/10 school like Caltech. THAT, to ME is where the cost vs academic/career/ROI tradeoff lies. In my opinion, there is a significant lifelong difference between a top Ivy (including Stanford) or technical type school (Caltech/MIT) and other schools. Not saying it's right, or an absolute, universal rule, but in general I think there's a significant enough of a difference in that tier of school to justify the added cost (AS LONG AS THAT SCHOOL IS A GOOD FIT FOR THE INDIVIDUAL) as mentioned before. If he hadn't gotten into one of those top in the country/world schools, he would be going where points 1 & 2 above led him and also where he wouldn't have to pay very much, if anything.
So my suggestion to you is to shoot for the moon and see how things play out. File for the FAFSA on October 1st, and go for any need based aid you can get at every school--you never know unless you ask. And many top private schools have huge financial endowments available. All it costs you is time doing the "paperwork". Also get his grades and test scores as high as possible - lots of academic aid out there from schools who want to lure HA candidates to bump up their academic numbers. In short, you want to give yourself as many good choices as possible then whittle them down according to points 1, 2 and 3 above.
Good luck, and try to enjoy the process along the way!