Hello Jim,
there is not much to go wrong with the starter carburettor, it is just a simple needle with a little air valve opened or shut with the solenoid. The sensor that switches it in and out (located in the inlet manifold water rail near to the thermostat) can be unreliable. The needle has an adjustable stop to set the mixture, down to weaken and up to richen. It runs with a very loud hiss so if your black smoke occurs when hot and you can't hear that hiss then it is unlikely that the starter carburettor is at fault.
Gummed up piston(s)could be the problem as Basil suggests or that one or both carburettors are flooding. Another problem I have encountered with HD6's is that the spring that controls the jet level corrodes and lets the jet drop.
In that situation the mixture adjusting screw has no effect as the spring does not push the jet up to the adjuster.
Unfortunately it is necessary to remove the carburettors to check this. The spring is in the base of the carburettor where the float chamber bolts to the main body.
good luck,
Alec /ubbthreads/images/graemlins/thirsty.gif