This may potentially be a programming issue related to fuel mapping consistent with the demands of the supercharger. As you may know, supercharged motors love fuel and ignition timing advance. Often times, supercharged motors have misfiring and detonation issues when the timing and fuel supply is not exactly perfect, especially under heavier loads (e.g., as you indicate at 3,500-4,000 RPMs).
At idle or when no boost is being supplied to the motor, the air/fuel ratio does not need to be as aggressive in order to maintain the proper supply of air and fuel to the motor. When more is demanded of the motor as you accelerate and the supercharger begins to produce additional boost, much more fuel and ignition timing is needed in order for this to happen effectively. When one or the other does not happen (i.e., too much ignition timing without the proper load of fuel), you will experience a misfire.
I recommend having a certified mechanic, such as one from YourMechanic, come to your location to determine why the engine is misfiring and suggest the needed repairs.
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