You need rubber grommets to screw the servo into. Otherwise, the servo vibrations will be amplified by the box that they're rigidly attached to.
Other possible quiet options:
- use a stepper motor -- no gearbox, can be very quiet! (especially if not microstepping or using PWM.)
- use a gravity pulley to run the gong strike. Use a small motor at some later time to wind the pulley again, when the noise doesn't matter.
- Use a spring to drive the gong strike, and use a motor to wind the spring, where you can more easily put the whole motor+spring assembly into a single box.
- Use a solenoid or other linear motor to drive the gong strike. If you start them softly, they make very little noise.