is the stumbling right at half throttle, or a bit below or above? if you mark the twist grip barrel at 1/4, 1/2, 3/4, and full rotation, you can figure out pretty closely which circuit is the one giving you trouble. the metering overlaps, and so a lean stumble at exactly half throttle could be the clip position, the needle taper, or lingering effects of the needle/needle jet diameter:
this old chart gives you an idea of which circuits dominate at which throttle positions:
"straight diameter" is referring to the size of the annulus between the straight portion of the needle and the needle jet. you can vary each independently to change that.
there are two screws-- the idle adjuster screw is knurled, up high on the body, and raises and lowers the slide to change the idle speed. and the idle air screw is brass with a slot, over by the bellmouth. it's just a needle-- turn it in to richen the mixture, and out to lean it.