If you hold a steady part-throttle position, does the stumble continue? If so, the accelsrator pump is not the problem. It only works to smooth out the transition from idle to part-throttle, etc. by squirting a little gas to prevent a lean condition while accelerating. It sounds like your carb has a lean condition at part-throttle, maybe an incorrect jet or metering rod, or a partially-plugged fuel passageway. Full throttle opens up more fuel passages or gets beyond the lean spot, solving the part-throttle stumble.
Jerry

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