Well, today I had time, so I took my scoot to the local mechanic and together we removed the clutch assembly and had a good look at it.
This is what we saw:

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Apparently, the clutch is of pretty low quality, and the clutch shoes are uneven and sloppily attached. The solution was simple: sandpaper them smooth and reinstall the clutch.
The effect has so far been amazing: no shivering and twitching at take off / low speed. The clutch disengages on time and has become very predictable, i.e. it doesn't pull the scoot when you get off throttle.
I'm very happy with the result and am very unhappy with the factory QC.
Will see how it behaves further on, good for now.