If he wants to go for a PHD (I realize this may change), he really should look into national LACs since they typically produce way more students who go on to PhD programs than large universities - this is due to their faculty being in part recruited for their ability to include undergrads into their research, when at large universities grad students will have the biggest responsibility, then often Honors College students or in specific Honors programs (for whom research may be a graduation requirement). In addition, the government research cuts made to large university research labs mean positions for undergrads will be even scarcer.
St Olaf, Lawrence, Kalamazoo are among those with high per capita PHD access and accessible for his GPA/test score (st Olaf probably target, Lawrence/Kalamazoo probably likely).
Lawrence&Kalamazoo don’t have anything religious-related.
(That being said, St Olaf isn’t "close-minded"religious - for instance, the first trans person who worked in the White House was a St Olaf grad. But it does have religion/ethics requirements so is likely out of the running).
Basically, colleges with 3-2 or 3-3 faculty contracts are going to have decent research opportunities.
If big time sports are a deal breaker, those^ wouldn’t work - undergraduate research access may not go hand in hand with large university sports. However a less exposed, less selective public university may be a good mix, allowing him to stand out and thus giving him a chance to join a lab and get research experience.
Beside being an auto admit to UIowa(+Honors), what about Pitt? It’s worth sending an application since they weigh test scores favorably (and their Honors College process would mean he may stand a chance there too, not sure about the research funding cuts there) and have rolling admissions so process applications quickly.
Other ideas in terms of large/medium universities:
UMaine Orono or USouthern Maine, UDel, App State?
Case Western would be a reach and no big time sports but Cleveland has excellent pro sports, could that substitute? And it’s a powerhouse for STEM.
ETA: saw above reply wrt Southern states.