Could the hesitation be the early warning signs of a plugged catalytic converter? That would possibly at least partially explain the acceleration problem, however why it somehow overcomes this at higher speed I am not sure. It would have been caused by an issue with the air/fuel mixture for a sustained period of time however, which means that the potentially plugged catalytic converter is only a symptom of another problem potentially related to that miss fire you were identifying at high engine speeds when manually controlling the throttle
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