The barrel adjuster is only for taking up a limited amount of cable slack. When you run out of adjuster room, turn the barrel adjuster back down to minimum thread, but do not bottom it out. Your clutch cable should now have some slack that needs to be taken out:
Look for the clutch lever on the bottom of the engine. The clutch cable goes to this lever and a bolt type cable clamp. To adjust, you loosen the bolt on the clamp (the right size wrench is in the tool kit that came with the scooter). grab the cable with some pliers and pull the slack out of it, then push the clamp up against the lever. Don't push the lever itself otherwise you will partly disengage the clutch when it is supposed to be fully engaged. Using your own third hand, a third hand tool, or a friend's hand, tighten the bolt. The clutch should be adjusted at this point. Now try riding. If you get that whining sound, and the gear change is more notchy than normal with the lever all the way out, then there is still too much slack.
Look for the clutch lever on the bottom of the engine. The clutch cable goes to this lever and a bolt type cable clamp. To adjust, you loosen the bolt on the clamp (the right size wrench is in the tool kit that came with the scooter). grab the cable with some pliers and pull the slack out of it, then push the clamp up against the lever. Don't push the lever itself otherwise you will partly disengage the clutch when it is supposed to be fully engaged. Using your own third hand, a third hand tool, or a friend's hand, tighten the bolt. The clutch should be adjusted at this point. Now try riding. If you get that whining sound, and the gear change is more notchy than normal with the lever all the way out, then there is still too much slack.