Miss a, this is not an answer from someone with massive amounts of knowledge and experience regarding Yeshivas in B’klyn, but from what I do know- Yeshiva Rabbayim here are overworked & their classrooms overcrowded. Unfortunately, most are not able to provide the kind of individualized attention you are implying your child needs. You will probably have an easier time getting your son accepted if you can offer to provide help for him yourself to bring him up to par with his peers; either by hiring a tutor (I know- great expense if you get someone good)or if he’s lucky enough to have a parent, grandparent, benevolent uncle, etc to help out. The Yeshiva staff might provide you with the name of a bachur who is able to help, but it won’t be free of charge in most cases.
It’s a pity that, as you wrote, smaller yeshivas, which sometimes seem attractive due to smaller classroom size, tend to provide much less education.
Good luck finding a place where you and your son will both be satisfied & happy. Hope it all works out!