black soot/smoke = oil or rich mixture?
I agree with most of the posts, that soot means you have too rich a condition. Just where that richness is is the tough question. We'll deal with the stumble at 1/4 throttle first. What's happening there is the engine is making the transition from the idle circuit to the main jet, and it's either running out of gas to help it over the change, or it has too much. I doubt it has too much at that point, most bigger engines will still pull with too much gas, although they may not be as sharp as they could be. Try following a car with a four barrel carb and watch the black smoke pour out of the pipe when the pedal gets mashed. Way too much fuel, yes, but no stumble.
You said you have the mid-range needle all the way down, clip in the top groove. What that does is lean out the transition from idle to main jet. Try raising it one step at a time. If it gets worse you need to go one size smaller on the main jet and start over.
As for the fuel screw, it should be on the bottom of the float bowl with the slotted head facing down, nasty place to get into. With the bike fully warmed up and idling, you need to turn it IN, counting the turns, thus leaning out the mixture, until the engine revs start to drop slightly and the idle gets rougher. This means the mixture is too lean. Now back it out, counting the turns, until the revs drop once again, and the engine gets rough again. Honda recommends a setting midway between these two points as a good place to leave it. I was always taught that you lean it out until the revs drop, then back it out again to get a good smooth idle. I've never had any problems doing it that way, but the manufacturer SHOULD know best.
If you can't get a reasonable idle, you may have to go back to the stock idle jet and try that. Once you have the idle nice and smooth, just set the idle speed as usual. I think once you clean up the mid-range and the idle, the main jet will be relatively easy to tune. The bike should pull cleanly up through the whole range. If it doesn't just take it one step at a time, and I can't stress strongly enough, only change one thing at a time, and make small adjustments before trying it. One thing you didn't mention was the spark plug... what does it look like as far as color goes? That can be your best indication if the engine is lean or rich. If you start seeing very light color deposits on the plug, you're dangerously lean. It should be a nice even dark tan color.
Good luck
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