There is some missing information. Is it Injected or carburated? I assume injected since it is an 06. Black smoke is a condition of not burning all the fuel going into the cylinder. This means too much fuel going in or not enough fire to properly ignite it. Start with new plugs, too much fuel could foul them. If it eliminates the problem and shows up again after a while your getting too much fuel. Secondly, running the choke too long during startup can foul the plugs as well. I would suggest diagnostics to really fix the problem.
As for the neutral issue, I had the same problem on my 05 Glide running HD Syn3. I could not find neutral no matter what, cold,hot ,running or not. I switched to Amsoil 75-110 in the tranny and 20-50 in the primary, now I find neutral every time. No clunking and shifts like butter.