I think there is a chart floating around the wiki on carburetor adjustments...and where they come into play.
If you look into the carb from the air filter side, you will see there is a notch cut into the slide. That angle cut comes into play around 1/8th to 1/4 throttle i believe...cant find chart and be exact.
The angle of the slide causes air to be directed toward the needle opening. so if your midrange is rich than you could very well have the wrong slide angle as well....moving the needle around may not matter until the slide is corrected.
Check out if slides, and different angles are available for your carb.
Most of the time it doesnt really matter when tuning a moped. mostly for people competing and need their exact power at every throttle open position.
I am not a carb expert so do your research. just some shit i read on wiki, in jennings...and so forth