Sorry about a slow answer, but I was in Wisconsin for a few days. My daughter got married Friday and I gave her away to what I think is a deserving man.
Now, the fuel screw is for idle only. It shouldn't affect acceleration, but if set too lean may contribute to popping in the exhaust. Most popping is caused by the mixture being too lean when the throttle is closed suddenly. Adding back pressure to the exhaust in on way to get rid of it, increasing restriction in the intake is another and increasing the idle speed will help too.
I'm trying to keep in mind that you have black smoke at full throttle. That usually indicates that the jetting is too rich at full throttle.
If you like speed and power, remember that "lean is mean!". A lean mixture produces more power than a rich mixture. A rich mixture burns cool and is easier to ignite. i.e. choking a cold motor to make it start. A lean mixture burns hot and that is what produces the best power. The power comes from the heat. And a fast burning (lower octane) fuel produces more power than a slow burning (high octane) fuel. The engine builder determines what octane fuel is best for the design. Honda usually recommends about 92 octane fuel demanded by their short stroke engine design. Here in the U.S., our 92 octane pump gas is diluted with alcohol which is high octane, but burns cool and has less BTU's per pound than gasoline. What we buy out of the pump is about an 84 octane gas with about 10 to 15% of ethanol added which derives a 92 octane rating but burns more like 100 octane. If you use a racing fuel without alcohol you will instantly realize an increase in power. Ask the guy with a Flex Fuel engine why he isn't using E-85 (85% ethanol). It might be cheaper at the pump, but the engine develops less power and gets lower mpg. I have heard that it actually costs more per mile to burn E-85, so the folks with the flex engines just use gas like everybody else.
When you get the jetting figured out, you will have a well performing machine. But pick a fuel and stay with it. I tried some $24 per gallon alcohol free racing fuel and while the engine performed better, I figured out that for my type of riding, I could live with the 92 octane pump gas, but I only use BP gas in my bike, I will use any old shit in my car and truck.
Maybe I should move to Alaska - they don't have alcohol in their gas. They don't have any ethanol producers in their state. Engines that get 40 miles to a gallon here get 50 mpg there.
I'll start with the air/fuel screw tonight, and see if there is a difference. Then I'll re-jet and see how it reacts to that... I'll keep you posted. 
