Is there someone in BMG you can talk to about it? I think part of the idea with the BTL is that you don’t necessarily need (many) other courses to get it and that it’s awarded by the yeshiva. (I know someone who is going to Harvard Law with only a BTL from his yeshiva- super rare these days especially, but it does seem to happen.)
For social work, you will probably need to take prereqs before applying/attending, no matter how you get the BTL- check with the grad programs you apply to to find out which.