Theoretically, I would encourage him to consider selecting the school that will best challenge him where he is weakest which will prepare him better for college. He doesn’t need a school to make him stronger where he is already strong. Any school on his list can do that. But, all of these schools require strong writing whether or not they have signature writing programs so, most likely, STEM vs. writing will not be the most useful final criteria.
Anecdote: Our son evaluated boarding schools based on film-making attributes. Two years in a row, he had taken first place in an annual digital filmmaking symposium at ASU while still in middle school. He lived with a camera in front of his face and was hell bent on USC’s film school, but he ended up in the military with an EE degree. Go figure. Moral of the story: BS is transformative in ways you can’t possibly imagine at this stage. Don’t focus too much on any single attribute. Boarding school is about the whole package and exploring lots of new things. If he has choices, I would simply allow your son to choose the school he likes best for whatever reason. They all deliver on so many levels. He will get as much STEM and writing as he can consume from any school on his list, and I don’t even have to see the list. 