The Queen of Persia-
Yeshiva Derech Chaim in Boro Park is a beis medrash that generally accepts good kids, even if they’re not top learners.
I do think all learning is done in English, though.
There are a couple of mesivtas in Flatbush that cater to boys who might be shvach learners or non-mainstream. I think Rabbi Rafael Walerstein and Rabbi Friedman (don’t remember his first name, but his yeshiva is on East 15th St. between J&K) are the ones who run the yeshivos. They may have some Beis Medrash ideas, since I would imagine some of their boys go on to learn full-time.
In my days there were several small “yeshivos” that were basically a rosh yeshiva/rebbe and maybe 10 boys learning in a shul. I don’t know of any specifically nowadays, but would it pay to look into something like that?