These are just a few ideas,
Could it be possible that when you accelerate too quickly you flood the carburetor? Maybe you need to upjet?
How's your air filter look? Maybe you aren't getting enough air to support the rush of gas from a quick accelaration? (If moped even work this way, I'm still learning these machines myself.)
Maybe you could have a problem in your clutch springs?
Again these are just ideas I'm no expert.
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