Converting A DC motor to ServoMotor

Why not have two solenoids in a push-pull config that would save the gear box, how big is the tank and plates. Maybe, and this just firing wildly in the dark an old washing machine motor as they usually have an agitation cycle which roughly approximates what you are after.

Instantly??

How do you define instantly? 10s, 1s, 1ms, ??
The shortest and easiest way, if you have compressed air, is the use of a pneumatic cylinder. Will be much faster, than any servo-AC-DC-whatever-motor.

The valves in F1 cars are driven by.............pneumatic system and they go verrrrrry fast 18 to 20.000 RPM equals 300 open/close cycle per second. Fast enough for you

Sorry didn't see the instant release part, maybe some sort of trip release with a cam to restore the flap or solenoid with a bar with multiple prongs. The motors wouldn't have to be too powerful as they only have to close the flaps.