The Slant is leaking from the Carter BBD

I think that is some kind of soft metal plug. If the gas seems to be coming out of there, well, that's your problem. I'm not sure how you would go about removing it non-violently. I would say use a torch but that seems inadvisable unless the carb was completely stripped down and ideally immersed in water. You could scrub it and try some JB Weld on the surface.